City-Scale Agent-Based Simulators for the Study of Non-Pharmaceutical Interventions in the Context of the COVID-19 Epidemic
Shubhada Agrawal, Siddharth Bhandari, Anirban Bhattacharjee, Anand Deo, Narendra M. Dixit, Prahladh Harsha, Sandeep Juneja, Poonam Kesarwani, Aditya Krishna Swamy, Preetam Patil, Nihesh Rathod, Ramprasad Saptharishi, Sharad Shriram, Piyush Srivastava, Rajesh Sundaresan, Nidhin Koshy Vaidhiyan, Sarath Yasodharan
11 City-Scale Agent-Based Simulators for theStudy of Non-Pharmaceutical Interventions inthe Context of the COVID-19 Epidemic
IISc-TIFR COVID-19 City-Scale Simulation Team ∗ Indian Institute of Science, Bengaluru † TIFR, Mumbai11 August 2020
Abstract
We highlight the usefulness of city-scale agent-based simulators in studying various non-pharmaceutical interventions to manage an evolving pandemic. We ground our studies in the contextof the COVID-19 pandemic and demonstrate the power of the simulator via several exploratory casestudies in two metropolises, Bengaluru and Mumbai. Such tools become common-place in any cityadministration’s tool kit in our march towards digital health.
Authors in alphabetical order of last names: Shubhada Agrawal † , Siddharth Bhandari † , Anirban Bhattacharjee † , AnandDeo † , Narendra M. Dixit ∗ , Prahladh Harsha † , Sandeep Juneja † , Poonam Kesarwani † , Aditya Krishna Swamy ∗ , PreetamPatil ∗ , Nihesh Rathod ∗ , Ramprasad Saptharishi † , Sharad Shriram ∗ , Piyush Srivastava † , Rajesh Sundaresan ∗ , Nidhin KoshyVaidhiyan ∗ , Sarath Yasodharan ∗ Corresponding author: Rajesh Sundaresan, [email protected]
PP, NR, SS, NKV, SY from IISc were supported by the IISc-Cisco Centre for Networked Intelligence, Indian Instituteof Science. RSun was supported by the IISc-Cisco Centre for Networked Intelligence, the Robert Bosch Centre for Cyber-Physical Systems, and the Department of Electrical Communication Engineering, Indian Institute of Science.TIFR co-authors acknowledge support of the Department of Atomic Energy, Government of India, under projectno. RTI4001.PH acknowledges support from the Swarnajayanti Fellowship of DST.RSap acknowledges support from the Ramanujan Fellowship of SERB.PS acknowledges support from the Ramanujan Fellowship of SERB, from Adobe Systems Inc. via a gift to TIFR, andfrom the Infosys-Chandrasekharan virtual centre for Random Geometry supported by a grant from the Infosys Foundation.The contents of this paper do not necessarily reflect the views of the funding agencies.Source code available at: https://github.com/cni-iisc/epidemic-simulator/releases/tag/3.0 a r X i v : . [ q - b i o . P E ] A ug Fig. 1:
Timeline of COVID-19 cases, recoveries and fatalities in India taken from [2]. See [2] and [3] fordetailed information on how COVID-19 progressed in India.
I. I
NTRODUCTION
COVID-19 is an ongoing pandemic that began in December 2019. The first case in Indiawas reported on 30 January 2020. The number of cases and fatalities have been on the risesince then. As on 11 August 2020, there are 22,68,675 cases (of which 15,83,489 haverecovered) and 45,257 fatalities [1]; see Figure 1 for a timeline of COVID-19 cases, recoveriesand fatalities in India. While medicines/vaccines for treating the disease remained under devel-opment at the time of writing this paper, many countries implemented non-pharmaceuticalinterventions such as testing, tracing, tracking and isolation, and broader approaches suchas quarantining of suspected cases, containment zones, social distancing, lockdown, etc. tocontrol the spread of the disease. For instance, the Government of India imposed a nation-wide lockdown from 25 March 2020 to 14 April 2020, and subsequently extended it until31 May 2020 to break the chain of transmission and also to mobilise resources (increasehealthcare facilities and streamline procedures). To evaluate various such interventions anddecide which route to take to manage the pandemic, epidemiologists resort to models thatpredict the total number of cases and fatalities in both the immediate and the distant futures.The models used should have enough features to enable the evaluation of the impact ofvarious kinds of non-pharmaceutical interventions.
Broadly three kinds of models have been used to study this epidemic. The first set ofmodels takes a curve-fitting approach. They rely on simple parametric function classes. Theparameters of the model are fit via regression to match observed trends. The second set ofmodels addresses the physical dynamics of the spread at a macroscopic level. These are mean-field ordinary differential equations (ODEs) based compartmental models (e.g. Susceptible-Exposed-Infected-Recovered (SEIR) model and its extensions) based on the classical workof Kermack and McKendrick [4]. Here the population is divided into various compartmentssuch as susceptible, exposed, infected, recovered, etc., based on the characteristics of theepidemic. One then solves a system of ODEs that captures the evolution of the epidemic ata macroscopic scale . Localised versions of these are spatio-temporal mean-field models thatlead to partial differential equations . The third set of models, and the focus of this work, areagent-based models . A very detailed model of the society under consideration, with as manyagents as the population, is constructed using census and other data. The agents interact invarious interaction spaces such as households, schools, workplaces, marketplaces, transportspaces, etc. See Figure 2 for a schematic representation of an agent-based model with theaforementioned interaction spaces. These interaction spaces are the primary contexts for thespread of infection. A susceptible individual can potentially get infected from an interactionin one of these spaces upon contact with an infected individual. Once an individual is exposedto the virus, this person goes through various stages of the disease, may infect others, andeventually, either recovers or dies. Other models work at an intermediate level by modellingthe social network of interactions, e.g., [12], but we shall focus more on agent based models.There are several advantages of using agent-based models. First, since modelling is per-formed at a microscopic level unlike the macroscopic level in compartmental models, agent-based models are well suited to capture heterogeneity at various levels. For instance, the age-dependent progression of COVID-19 in individuals (severity, the need for hospital care, in-tensive care, etc.) can be incorporated in agent-based models. Second, individual behaviouralchanges, known to be important in certain diseases such as AIDS, can be easily modelled.Third, agent-based models are well suited to study the impact of various non-pharmaceuticalinterventions, such as “lockdown for a certain number of days”, “offices operating using the See [5] for a state-level epidemiological model for India and [6] for a combination of the two approaches. For a paper in the Indian context see [7]. There are other agent-based simulators that have informed policy decisions. See [8] for UK and USA related studiesspecific to COVID-19, see [9] for a COVID-19 study on Sweden, see [10] and references therein for many agent-basedmodels and their comparisons, and see [11] for a taxonomy of agent-based models.
Fig. 2:
Schematic representation of an agent-based model. (so-called) odd-even strategy”, “social distancing of the elderly”, “voluntary home quaran-tine”, “closure of schools and colleges”, etc. Explicit modelling of these contexts of infectionspread also enables studies of control measures targeting the interaction spaces. Fourth, thereis an important difference between the actual infected number in the population, which iswhat the differential equations-based models predict, and the reported cases . The latter isinvariably based on those that come to hospitals/clinics seeking health care, or those thatare identified due to random testing, followed by contact tracing of such index cases. Asa consequence, reported cases provide a biased estimate of the actual infected number inthe population. Agent-based simulators have the capability to track such biased estimates ofprevalence.In this work, we describe our city-scale agent-based simulator to study the epidemic spreadin two Indian cities and demonstrate how digital computational capabilities can help us assessthe impact of various interventions and manage a pandemic.We now provide sample outcomes for Bengaluru and Mumbai for COVID-19 under variousinterventions. These outcomes have been generated using our city-scale agent-based simulator.Bengaluru and Mumbai have estimated populations of 1.23 and 1.24 crore people respec-
Fig. 3:
A timeline of Bengaluru interventions. tively , and our simulator has instantiated those many agents. The Bengaluru population isspread over 198 administrative units called wards. Similarly the Mumbai population is spreadover similar administrative units or wards, but there are 24 such wards in Mumbai. Since theseare larger wards compared to Bengaluru’s wards, there is significant variation of populationdensity within each ward in Mumbai. To model higher spread in densely populated areas,each of the 24 wards is modelled to have subareas with denser population.
1) Bengaluru:
For Bengaluru, we consider the following scenario. The Government ofIndia implemented a 40-day lockdown starting 25 March 2020. Bengaluru and Karnataka hadalready closed some interaction spaces in the form of a pre-lockdown. After the 40-daylockdown, there was a phased opening of various activities and offices. More details are asfollows. These can also be read from Figure 3. We then provide a simulation outcome forthese interventions and compare them with the actual situation on the ground. The details: • Pre-lockdown from 14–24 March 2020, the first shaded region in Figures 5–6. •
40 days of lockdown from 25 March – 03 May 2020, the second and the third shadedregions in the figures. •
14 days of phased opening from 04–17 May 2020 involving voluntary home quarantine, The 2011 census figure for Bengaluru is 0.85 crore and for Mumbai is 1.24 crore (Mumbai city only, not the MumbaiUrban Area whose 2011 census estimate is 1.84 crore). Bengaluru’s 2020 population is estimated to be 1.23 crore. Reliabledata is not available for Mumbai city’s 2020 population. We have used 2020 estimated population for Bengaluru and 2011census estimate for Mumbai. social distancing of the elderly, closure of schools and colleges, 50% occupancy atworkplaces, and case isolation. This is the fourth shaded region in the plots. • From 18 May 2020 onwards, continued contact tracing (following the Indian Councilof Medical Research (ICMR) guidelines as much as possible) and associated quarantin-ing and case isolations, but otherwise an unlocked Bengaluru.
Soft ward containment continues to be in force. By soft ward containment, see Figure 4, we mean linearly-varying mobility control that turns an open ward into a locked ward when the number ofhospitalised cases become 0.1% of the ward’s population; in the latter locked scenario,only 25% mobility is allowed for essential services. • Past studies [13]–[16] have indicated that masks have been effective in reducing thespread of influenza. Anecdotal evidence seems to suggest that masks are effectivefor COVID-19. The Ministry of Home Affairs (MHA) order of 15 April 2020 [17,Annexure 1] made the wearing of masks in public places compulsory. This was re-emphasised in the MHA order of 30 May 2020 [18]. We assume that masks are mandatoryfrom 09 April 2020 onwards. • It is often the case that when there are several restrictions in place, only a fraction ofthe population complies with these restrictions. Getting the entire population to complyis often a big challenge and requires significant and persistent messaging (includingcommunication, rewards, punitive measures). We assume a compliance factor of 0.7up to 04 May 2020, which means that 70 percent of the population adheres to thegovernment guidelines like social distancing, wearing masks in public places, etc., and0.6 thereafter. The reduction could be attributed to behavioural changes due to lockdownfatigue. • A brief lockdown during 14–21 July 2020 was implemented in Bengaluru. We comparetwo scenarios, one with this lockdown and one without this lockdown.As one can anticipate, simulation of the above scenarios requires a significant level ofsophistication in the modelling and implementation. We describe how we do these in thecoming sections, but now focus only on the outcomes.Figure 5 estimates the daily positive cases and Figure 6 estimates the daily fatalities directlydue to COVID-19 in Bengaluru. In both these plots, we compare our estimates with thesituation on the ground. The plots are the means of 5 runs each on two versions of syntheticBengaluru. The jaggedness is due to the stochasticity associated with the limited number ofruns. For greater clarity, we have not included the standard error plots.Figure 5 and Figure 6 provide the estimates with and without this one-week lockdown.
Fig. 4:
Wards are contained in a ‘soft’ way. The mobility is gradually decreased based on the signal of numberof hospitalised cases in the ward. When 1 in 1000 in the ward is hospitalised, a local lockdown comes intoeffect.
Fig. 5:
Bengaluru daily positive cases estimation. The red bars are the reported cases. The five shaded regionsbetween 14 March and 01 June represent the durations of the various lockdown phases. The shaded regionaround 15 July represents a short one-week lockdown. For cumulative case plots, see Figure 11.
The trend for the reported cases is roughly captured, but fatalities are over-predicted. This issurprising since the reported cases continued to be high in the third week of July. For a moredetailed study of these plots, we refer the reader to Section III-A. At this stage, we onlyobserve that the public health benefit of the lockdown is clear from the pictures, reduced
Fig. 6:
Bengaluru daily fatalities estimation. For cumulative fatalities, see Figure 12 in a later case study. peak at the expense of a brief second wave. Armed with these predicted outcomes under thetwo scenarios, public health officials can now weigh the benefits of the lockdown against itseconomic consequences.
2) Mumbai:
For Mumbai, we simulate the following scenario. • A pre-lockdown similar to Bengaluru, but during 16-24 March 2020 (first shaded regionin Figure 7-8). • • Masks are mandatory from 09 April 2020. • Workplaces open with a small strength of 5% during 18-31 May 2020, as per Governmentof Maharashtra directions. This is the fifth shaded region. During this period, socialdistancing of the elderly and school and college closures remain in force. • Workplace strengths increase to 20% in June, to 33% in July, and to 50% in August,with commensurate capacity increases in the local trains. Social distancing of the elderlyand school and college closures remain in force. In addition voluntary home quarantineand case isolation come into play. • Throughout the simulations, soft ward containment is in force. • It is often difficult to comply with social distancing directives in high population densityareas, like in slums, with many common essential facilities. In Mumbai, we model
Fig. 7:
Mumbai daily positive cases estimation. The five shaded regions between 16 March and 01 Junerepresent the durations of the various lockdown phases in Mumbai. For cumulative case plots, see Figure 21. compliance to be 0.4 in high density areas and 0.6 in other areas. • Throughout the simulations, contact tracing, associated quarantining, testing, and furthertracing are enabled. • We will compare the above scenario, with local trains enabled, and will contrast it withanother hypothetical scenario having no local trains.Figure 7 estimates the daily positive cases and Figure 8 estimates the daily fatalities. Inboth these plots, we compare our estimates with the situation on the ground. Again the plotsare the means of five runs each on two synthetic versions of Mumbai.But for a delay in the estimated cases curve, the trends for cases and fatalities are capturedwell. The delay in the estimated cases is perhaps due to delayed reporting which is notmodelled in the simulator. From these figures, one can recognise the usefulness of the agent-based simulator in assessing the impact of opening of the local trains in Mumbai.
Agent-based simulator – an important intervention-planning tool : Let us summarise theoutcomes of the above two examples. We saw the public health impact of imposing a shortlockdown in Bengaluru. We also saw the impact of opening up trains vs. keeping the trainsnon-operational in Mumbai. Such comparisons that can inform better on-ground decisionmaking are enabled by a city-scale agent-based simulator. This capability arises mainlybecause of the enhanced modelling and control of the interaction spaces in the simulator. It Fig. 8:
Mumbai daily fatalities estimation vs. corrected fatality time series, as corrected by BMC on 18 June2020. For cumulative fatalities, see Figure 22 in a later case study. is our hope that such tools become common place in a city administration’s tool kit, and areused to the fullest extent before drastic interventions with wide-scale impact, e.g., lockdown,are imposed. With additional modelling of activity, mobility, and behaviour, and use of highquality data on the migrant labour force in urban areas, we speculate that we could haveanticipated certain behavioural outcomes seen in India after the lockdown announcement(e.g., migrant population movement).II. M
ETHODOLOGY : A
GENT - BASED MODELLING
Broadly, the steps involved in agent-based modelling are the following: build the simulator,calibrate it, validate it, and use it for estimating how the pandemic will evolve.1.
Simulator . The simulator itself consists of four parts.
Synthetic city . A synthetic city generator builds a synthetic city with individuals andvarious interaction spaces. Individuals are assigned to various interaction spaces such ashouseholds, schools/workplaces, communities and transport spaces. In doing this we capturethe demographics of the city, the school size distributions, the workplace size distributions,the commute distances, the neighbourhood and friends’ interaction networks, the transportinteraction spaces, etc. These fix the “social networks” on which individuals interact andtransmit the virus. Disease progression . A disease progression model that involves the biology of the diseasethen indicates what is the incubation period, infective period, symptomatic period, severityof the symptoms, viral load, virus shedding, health care and in-hospital progression, etc.
Interactions and evolution . The level of infectivity during the infective period, the durationof the infective period, and the social network interactions in the various interaction spacesdetermine how the disease evolves in the city. We start the simulator with a certain numberof infected individuals. They then interact with susceptible individuals at various interac-tion spaces, who in turn interact with other susceptible individuals, and thus the epidemicprogresses. The key parameters in the disease evolution are the transmission coefficientsassociated with each interaction space that model the chance of meetings and disease spreadin that interaction space.
Intervention model . Various kinds of intervention policies need to be defined and theirimpact on transmission coefficients should be modelled. See Table I for some examples. Manyof these involve reduction in changes in contact rates as a consequence of the interventions.The values to set could be based on observed mobility patterns. For example, according tothe COVID-19 Community Mobility Report for India in April [19] in Table II, prepared byGoogle based on data from Google Account users who have “opted-in” to location history,there was significant reduction in mobility during the lockdown period compared to thebaseline period of 03 January 2020 to 06 February 2020. This informs the nominal contactrate choices in the interventions’ definitions in Table I and later in other Tables.TABLE I: Intervention modelling
Label Policy DescriptionCI Case isolation at home Symptomatic individuals stay at home for 7 days, non-household contactsreduced by 90% during this period, household contacts reduce by 25%.HQ Voluntary home quarantine Once a symptomatic individual has been identified, all members of thehousehold remain at home for 14 days. Non-household contacts reducedby 90% during this period, household contacts reduce by 25%.SDO Social distancing of thoseaged 65 and over Non-household contacts reduce by 75%.LD Lockdown Closure of schools and colleges. Only essential workplaces active. For acompliant household, household contact rate doubles, community contactrate reduces by 75%, workspace contact rate reduces by 75%. For a non-compliant household, household contact rate increases by 25%, workspacecontact rate reduces by 75%, and no change to community contact rate. TABLE II: Mobility report generated on 11 April 2020, see [19].
Place ReductionRetail and recreation -80%Grocery and pharmacy -55%Parks and public plazas -52%Public transit stations -69%Workplaces -64%Residential +30% Calibration . Once the simulator is ready there are still unknown parameters that needto be identified. These include the contact rates at various interaction spaces, the numberof infections to seed, the time at which these infections should be seeded, the complianceparameters, etc. The purpose of the calibration step is to identify these parameters to capturethe city specific trends and contact rates. We do this by choosing the initial number to seed,the time at which these are seeded, and the contact rates so that the initial trend of thedisease is matched. Once calibrated, we can run our simulator for a certain number of daysand understand how the epidemic spreads.3.
Validation . We next have to validate our simulator, so that we can understand thepredictive power of the simulator. For this, we look for phenomena in the real data thathave not been explicitly modelled and we check if the simulator is able to capture thesephenomena. For specific details, see Section IV.4.
Use of the simulator in an evolving pandemic . It is often the case that in evolvingpandemics, predictions do not match reality as time unfolds. Models are often gross over-simplifications of the underlying complex reality and assumptions are often wrong or mayneed updating as the pandemic evolves. The purpose of models in an evolving pandemicis not merely to predict numbers, in which task they will likely fail, but more to enableprincipled decision making on intervention strategies. They enable a study of the publichealth outcomes of one strategy versus another. Armed with these comparisons, public healthofficials can make more informed decisions. Needless to say, these are often more complexand involve several aspects beyond just public health, e.g. economy, psychology, education,political climate, to name a few . For a proposal on how to simulate economic and public-health aspects together, see [20]. III. D
ESIGN OF INTERVENTIONS VIA CASE STUDIES
One of the powerful features of the agent-based simulator is its ability to explicitly controlvarious interaction spaces and study the outcomes. We demonstrate this feature via the casestudies for Bengaluru and Mumbai listed in Table III.TABLE III: Case studies for Bengaluru and Mumbai
Case Study Title SectionCase Study A No intervention (but only contact tracing-based isolation) versuslockdown versus the current scenario in Bengaluru Section III-ACase Study B Impact of opening offices at 50% capacity with higher compli-ance versus lockdown at lower compliance, a Bengaluru study Section III-BCase Study C Impact of opening trains versus not opening trains in Mumbai Section III-CCase Study D Soft ward containment versus neighbourhood containment inBengaluru Section III-DCase Study E Soft ward containment at various levels in Mumbai Section III-ECase Study F Schools/colleges open from 01 September 2020 in Bengaluru Section III-F
A. Case Study A: No intervention (but only contact tracing-based isolation) versus lockdownversus the current scenario in Bengaluru
We compare the following three scenarios in Bengaluru: • No intervention other than contact tracing, testing and associated case isolation. • Indefinite lockdown starting from 14 March 2020 onwards. This naturally will haveenormous economic and societal cost, but we focus only on the direct COVID-19 publichealth outcomes. • Scenario-2 in Table IV: soft ward containment, case isolation with testing and contacttracing, and a one-week lockdown during 14–21 July 2020.We assume a compliance of 70% until 03 May 2020 (i.e. during the initial Karnataka-widelockdown followed by the nation-wide lockdown) and a compliance of 60% starting 04 May2020, for all these scenarios. That is, 70% (resp. 60%) of the population comply with therestrictions in place until 03 May 2020 (resp. starting 04 May 2020). Under these scenarios,we plot the following: daily cases (Figure 9), daily fatalities (Figure 10), cumulative cases(Figure 11), cumulative fatalities (Figure 12) and estimated hospital beds and critical carebeds (Figure 13). We make the following observations. TABLE IV: Simulated Bengaluru interventions
Period Scenario-1 Scenario-2 Compliance01 – 13 March 2020 No intervention No intervention NA14 – 24 March 2020 Prelockdown Prelockdown 70%25 March – 03 May 2020 40 days of National lockdown 40 days of National lockdown 70%09 April 2020 – onwards Masks ON Masks ON 60%04 – 17 May 2020 Phased opening. Voluntary homequarantine, social distancing of el-derly, case isolation, schools andcolleges closed, 50% occupancy atworkplaces. Phased opening. Voluntary homequarantine, social distancing of el-derly, case isolation, schools andcolleges closed, 50% occupancy atworkplaces. 60%18 May – 11 July 2020 Unlocked Bengaluru with onlyICMR-guideline contact tracingand associated quarantining andcase isolations, social distancing ofelderly, case isolation, schools andcolleges closed. Unlocked Bengaluru with onlyICMR-guideline contact tracingand associated quarantining andcase isolations, social distancing ofelderly, case isolation, schools andcolleges closed. 60%12 – 13 July 2020 Same as above Prelockdown - 50% mobility 60%14 July – 21 July 2020 Same as above Bengaluru lockdown 60%22 July – 31 July 2020 Same as above Case isolation, social distancing ofelderly, school closure, workplaces at50% 60%01 August 2020 – onwards Same as above Case isolation, social distancing ofelderly, school closure, workplaces at100% 60%Throughout Soft ward containment enabled Soft ward containment enabled 60% • As one would expect, the least number of cases, fatalities and hospital beds requirementscorrespond to the “indefinite lockdown” scenario. However this scenario has seriousimpact on the economy, livelihoods, etc. • In terms of the daily number of cases, the no intervention scenario had a peak around01 June 2020 (with roughly 15,000 cases), whereas the present scenario in Bengaluru(i.e. Scenario-2 in Table IV) had a much lower peak around 15 July 2020 (with around2000 cases), followed by another peak around end of August. Similar trends can beseen in the fatalities estimates as well as the hospital bed estimates. Our health caresystem would have struggled with the no intervention scenario, and the present scenarioin Bengaluru helped mitigate and delay the peak of the epidemic. • The second predicted peak in Scenario-2 in Table IV is due to the one-week lockdown Fig. 9:
Case study A, subsection III-A: Bengaluru daily cases estimation. For a magnified view of the lowerpart of the plot, see Figure 5. The no-intervention situation would have overwhelmed the healthcare systemmany times over. during 14–21 July 2020. • Towards the end of July, we overpredict the number of daily fatalities and underpredictthe number of daily cases. This could be because of two reasons:1) The number of tests has increased significantly during mid-July due to whichthere is a likely surge in the number of asymptomatic cases. As a consequence,a reduction in the number of daily cases due to the one-week lockdown during14–21 July is not observed in the reported number of daily cases; such a reductionis visible in our estimates because the testing regime is assumed constant throughthe period in our simulator.2) There is a delay in reporting the fatalities. As the reported number of daily casesfollow an exponential trend during early-mid July, one would expect a similartrend in the reported daily fatalities during end-July, as shown in our prediction ofthe daily fatalities under Scenario-2. However, we see a reduction in the reportednumber of daily fatalities during after 15 July 2020. This could be due to a possibledelay in reporting the daily fatalities, or an effective use of the rapid point-of-careantigen test kits, or a combination of both. Testing of these hypotheses requirefurther investigation. Fig. 10:
Case study A, subsection III-A: Bengaluru daily fatalities estimation. For a magnified view of thelower part of the part, see Figure 6.
Fig. 11:
Case study A, subsection III-A: Bengaluru cumulative cases estimation. Fig. 12:
Case study A, subsection III-A: Bengaluru cumulative fatalities estimation.
Fig. 13:
Case study A, subsection III-A: Bengaluru hospital beds estimation. ‘Hospital Beds’ refers to thenumber of beds occupied for regular care including possibly oxygen support. ‘ICU Beds’ refers to those thatneed intensive care or ventilation. The no-intervention scenario would have overwhelmed Bengaluru’s healthcaresystem. B. Case Study B: Impact of opening offices at 50% capacity with higher compliance versuslockdown at lower compliance
The degree of compliance among the population to public health directions/guidelines isan important factor that affects the epidemic. To understand the importance of compliance,we compare the following scenarios for Bengaluru: the present Bengaluru (i.e. Scenario-2 inTable IV), an unlocked Bengaluru (i.e. Scenario-1 in Table IV), and an unlocked Bengaluruwith a higher compliance of 90% starting 04 May 2020 (i.e. Scenario-1 in Table IV with70% compliance during 14 March 2020 – 03 May 2020 and 90% compliance starting 04 May2020). As before, we plot the following: daily cases (Figure 14), daily fatalities (Figure 15),cumulative cases (Figure 16), cumulative fatalities (Figure 17) and estimated hospital bedsand critical care beds (Figure 18). We make two important observations: • In terms of the number of cases and fatalities, the present Bengaluru (i.e. Scenario-2in Table IV) with 60% compliance starting 04 May 2020 is worse than an unlockedBengaluru with 90% compliance starting 04 May 2020 (with both scenarios having70% compliance until 03 May 2020). While the qualitative outcome is not surprising,the quantitative estimates suggest just how important compliance is in curbing thespread of the disease. Armed with such comparisons, city administrations could suitablyallocate resources for communication, awareness, and other such campaigns to educatethe general populace on the public health impact of their actions, to induce more pro-social behaviour, and to ensure greater compliance. This was the approach taken bySweden, a country with a population of about 1 crore. • Comparing Scenario-1 and Scenario-2, we see that the effect of the one-week lockdownduring 14–21 July is very minimal in the long term as far as the cumulative numberof cases and fatalities are concerned. However, there is a significant difference in thecumulative number of cases and fatalities between Scenario-2 and Scenario-1 witha higher compliance of 90% starting 04 May 2020. This suggests that, given thatvaccines for COVID-19 are not yet available, short-term lockdowns’ benefit is restrictedto mobilising resources and preparing the healthcare system in the short term. On theother hand, higher compliance has a greater impact in reducing cases and fatalities. Fig. 14:
Case study B, subsection III-B: Bengaluru daily cases estimation.
Fig. 15:
Case study B, subsection III-B: Bengaluru daily fatalities estimation. Fig. 16:
Case study B, subsection III-B: Bengaluru cumulative cases estimation.
Fig. 17:
Case study B, subsection III-B: Bengaluru cumulative fatalities estimation. Fig. 18:
Case study B, subsection III-B: Bengaluru hospital beds estimation. C. Case Study C: Impact of opening trains versus not opening trains in Mumbai
TABLE V: Simulated Mumbai interventions
Period Interventions Attendance atworkplaces Compliancein non-slums Compliancein slums01 March – 15 March 2020 No Intervention at 100% capacity 60% 40%16 March – 08 April 2020 Lockdown Essential services oper-ate at 100% capacity,others are closed 60% 40%09 April – onwards Masks ON09 April – 30 April 2020 Lockdown Essential services oper-ate at 100% capacity,others are closed 60% 40%01 May – 17 May 2020 Lockdown with socialdistancing of the elderly Essential services oper-ate, others are closed 60% 40%18 May – 31 May 2020 Social distancing of theelderly, school closure,community factor=0.75 Essential services oper-ate at 100%, others op-erate at 5% capacity 60% 40%01 – 30 June 2020 Home quarantine,social distancing ofthe elderly, schoolclosure, trains ON,community factor=0.75 Essential services oper-ate at 100%, others op-erate at 20% capacity 60% 40%01 – 31 July 2020 Same as above Essential services oper-ate at 100%, others op-erate at 33% capacity 60% 40%01 August onwards Same as above Essential services oper-ate at 100%, others op-erate at 50% capacity 60% 40%
Throughout Soft ward containmentenabled
We now study the impact of opening suburban trains in Mumbai. Table V shows the time-line of various restrictions implemented in Mumbai starting from 01 March 2020. Suburbantrains were not under operation in Mumbai during 15 March – 31 May 2020. As suburbantrains are a key mode of daily commute in Mumbai, we compare the situation in Table Vunder two scenarios: • Trains-ON: Suburban trains are operational starting 01 June 2020 in a phased manner,similar to the opening of workplaces in a phased manner as indicated in Table V, Fig. 19:
Case study C, subsection III-C: Mumbai daily cases estimation.
Fig. 20:
Case study C, subsection III-C: Mumbai daily fatalities estimation. • Trains-OFF: Suburban trains are not operational throughout.As indicated in Table V, we assume a compliance factor of 60% in non-slums and 40% inslums. We plot our results in Figures 19-23. • From the plots, we see that the phased opening of suburban trains starting 01 June 2020gives a marginal increase in the number of cases, fatalities and hospital beds comparedto the Trains-OFF scenario. This suggests that trains can be operated with enforcement Fig. 21:
Case study C, subsection III-C: Mumbai cumulative cases estimation.
Fig. 22:
Case study C, subsection III-C: Mumbai cumulative fatalities estimation. of strict physical distancing (by operating at reduced passenger loads ) and compulsorywearing of face masks. Physical distancing under normal passenger loads in Mumbai locals is not possible given the large number of commutersper train. Fig. 23:
Case study C, subsection III-C: Mumbai hospital beds estimation. • Although we match the daily fatalities curve very well, we over-predict the daily numberof cases. We believe that this is due to the limitation on the testing capacity on the ground.Because of this, the test results of many people arrive late and cases get reported with acertain delay. It is also worth mentioning that, although we overpredict the daily numberof cases, we correctly capture the growth rate of the daily number of cases as well asthe cumulative number of cases. D. Case study D: Soft ward containment versus neighbourhood containment
We study the impact of two containment strategies for Bengaluru: soft ward containment(i.e., linearly-varying mobility control that turns an open ward into a locked ward whenthe number of hospitalised cases become 0.1% of the wards population; in the latter lockedscenario, only 25% mobility is allowed for essential services, see Figure 4) and neighbourhoodcontainment (i.e., when an individual is hospitalised, everyone living in a 100m surroundingarea undergoes home quarantine). Soft ward containment is a more feasible strategy thanstrict ward containment since the average ward population in Bengaluru is about 62,000. As We use a corrected version of the reported number of daily fatalities from Brihanmumbai Municipal Corporation (BMC).The initial reported daily fatalities curve from BMC had a very large peak at 16 June 2020. The corrected data adjuststhe daily fatalities curve until 15 June 2020 so that the peak on 16 June 2020 gets re-distributed to the previous days in asuitable way. Fig. 24:
Case study D, subsection III-D: Bengaluru daily cases estimation.
Fig. 25:
Case study D, subsection III-D: Bengaluru daily fatalities estimation. the number of hospitalised cases in the ward increases, more public health wardens could bedeployed and help reduce mobility and interaction in the ward.In Figures 24-28, we plot these two scenarios. We observe that neighbourhood containmentis more effective than soft ward containment, in terms of cases and fatalities. Fig. 26:
Case study D, subsection III-D: Bengaluru cumulative cases estimation.
Fig. 27:
Case study D, subsection III-D: Bengaluru cumulative fatalities estimation. Fig. 28:
Case study D, subsection III-D: Bengaluru hospital beds estimation. E. Case Study E: Soft ward containment at various levels in Mumbai
To compare various levels of strictness with which policies are enforced, we now considerthe opening scenario indicated in Table V and vary the containment leakage to see how thisaffects the numbers. Containment leakage stands for the level of activity that is allowed in award under containment. A strict enforcement would not allow more than 10% of the normalactivity. The case of ‘no enforcement’ results in activity at 100% of the original level; thiscorresponds to no adaptation in containment as a function of the number of hospitalisationcases. We explore various values of containment leakage and plot results for 10%, 25%, 50%and 100%.Figures 29-33 represent the (simulated) number of daily cases, cumulative cases, dailyfatalities, cumulative fatalities and daily hospital bed estimates, respectively, for the varyingcontainment leakages. These plots demonstrate how an effective containment policy (even aslow as 50%) can significantly reduce the number of cases, fatalities and hospital beds.An interesting observation is that, for the 25% leakage case, our simulator matches thelinear growth trend of the daily and cumulative number of cases as well as fatalities. Thelinearity is a likely consequence of the specific soft ward containment policy, triggered by thehospitalisation cases, i.e., mobility is reduced linearly with the number of hospitalisations inthat ward. It is not clear to what extent differential equation models can capture such lineartrends. Fig. 29:
Case study E, subsection III-E: Mumbai daily cases estimation. Fig. 30:
Case study E, subsection III-E: Mumbai daily fatalities estimation.
Fig. 31:
Case study E, subsection III-E: Mumbai cumulative cases estimation. Fig. 32:
Case study E, subsection III-E: Mumbai cumulative fatalities estimation.
Fig. 33:
Case study E, subsection III-E: Mumbai hospital beds estimation. F. Case Study F: Bengaluru with schools/colleges open from 01 September 2020
We now study the impact of opening schools. In Figures 34–38, we compare the followingtwo scenarios: • Schools-closed: The present scenario in Bengaluru, i.e., Scenario-2 in Table IV, • Schools-open: Scenario-2 in Table IV with schools open from 01 September 2020.As expected, both these scenarios follow the same trend until about mid-September, afterwhich the disease spread increases in the latter. Around early November, we observe abetween 10-15% increase in the cumulative number of cases and the cumulative numberof fatalities due to the opening of schools. This could be weighed with other factors suchas the capacity of our healthcare system to handle the rise, the impact of mental health ofstudents due to extended closures, etc., while arriving at a decision on whether schools canbe opened from 01 September 2020. The proportion of additional children and adults affecteddue to the opening of the schools is still under study.Fig. 34:
Case study F, subsection III-F: Bengaluru daily cases estimation. Fig. 35:
Case study F, subsection III-F: Bengaluru daily fatalities estimation.
Fig. 36:
Case study F, subsection III-F: Bengaluru cumulative cases estimation. Fig. 37:
Case study F, subsection III-F: Bengaluru cumulative fatalities estimation.
Fig. 38:
Case study F, subsection III-F: Bengaluru hospital beds estimation. IV. S
IMULATOR
A. City generation
The first step in our agent-based model is to model a synthetic city that respects thedemographics of the city that we want to study. Our city generator uses the following dataas input: • Geo-spatial data that provides information on the wards of a city (components) alongwith boundaries. (If this is not available, one could feed in ward centre locations andward areas). • Population in each ward, with break up on those living in high density and low densityareas. • Age distribution in the population. • Household size distribution (in high and low density areas) and some information onthe age composition of the houses (e.g., generation gaps, etc.) • The number of employed individuals in the city. • Distribution of the number of students in schools and colleges. • Distribution of the workplace sizes. • Distribution of commute distances. • Origin-destination densities that quantify movement patterns within the city.Taking the above data into account, individuals, households, workplaces, schools, transportspaces, and community spaces are instantiated. Individuals are then assigned to households,workplaces or schools, transport and community spaces, see Figure 2 for a schematic repre-sentation. The algorithms for the assignments do a coarse matching. The matching may berefined as better data becomes available.The interaction spaces – households, workplaces or schools, transport and communityspaces – reflect different social networks and transmission happens along their edges. Thereis interaction among these graphs because the nodes are common across the graphs, seeFigure 39 for various interaction spaces and Figure 40 for a bipartite graph abstractions ofthese interaction spaces. An individual of school-going age who is exposed to the infectionat school may expose others at home. This reflects an interaction between the school graphand the household graph. Similarly other graphs interact.We now describe how individuals are assigned to interaction spaces.
Individuals and households : N individuals are instantiated and ages are sampled accordingto the age distribution in the population. Households (based on the N and the mean number Fig. 39:
Various interaction spaces, solid circles inside homes indicate individuals.
Fig. 40:
Bipartite graph abstraction of interaction spaces. per household) are then instantiated and assigned a random number of individuals sampledaccording to the distribution of household sizes. An assignment of individuals to householdsis then done to match, to the extent possible, the generational structure in typical households.The households are then assigned to wards so that the total number of individuals in theward is in proportion to population density in the ward, taken from census data. A populationdensity map is given in Figure 41(a) for Bengaluru and in Figure 41(b) for Mumbai. Thegenerational gap, household distribution, and age distribution patterns are assumed to beuniform across the wards in the city. Each household in a ward is then assigned a random (a) Bengaluru. (b) Mumbai. Fig. 41:
Population density maps of Bengaluru and Mumbai. location in the ward, and all individuals associated with the household are assigned the samegeo-location as the household.Based on the age and the unemployment fraction, each individual is either a student or aworker or neither.
Assignment of schools : Children of school-going ages 5-14 and a certain fraction of thepopulation aged 15-19 are assigned to schools. These are taken to be students. The remainingfraction of the population aged 15-19 and a certain fraction of the population aged 20-59,based on information on the employed fraction , are all classified as workers and are assignedworkplaces. The rest of the population (nonstudent, unemployed) is not assigned to eitherschools or workplaces.In past works, given the structure of educational institutions elsewhere, educational insti-tutions have been divided into primary schools, secondary schools, higher secondary schools,and universities. The norm in Indian urban areas is that schools handle primary to highersecondary students and then colleges handle undergraduates. We view all such entities asschools.We assign students to schools on a ward-by-ward basis. In each ward, we have a certainnumber of students. We pick a school size from a given school size distribution and instantiate The unemployed fraction in Bengaluru, from the census data, is just over 50%, even after taking into account employmentin the unorganised sector. Similar is the case with Mumbai. This may have some bearing on the epidemic spread. a school of this size and place it randomly in that ward. Students who live in that ward arepicked randomly and assigned to this school until that school is filled to its capacity. Werepeat this procedure until all students in that ward gets assigned to a school, and then werepeat this procedure for all wards. This procedure could lead to at most one school per wardwhose capacity is more than its sampled capacity. Assignment of workplaces : Workplace interactions can enable the spread of an epidemic.In principle, Bengaluru’s and Mumbai’s land-use data could be used to locate office spaces.The assignment of individuals to workplaces is done in two steps. In the first step, foreach individual who goes to work, we decide the ward where his/her office is located. Thisassignment of a “working ward” is based on an Origin-Destination (OD) matrix. An ODmatrix is a square matrix whose number of rows equals the number of wards, and its ( i, j ) thentry tells us the fraction of people who travel from ward i to ward j for work. In the secondstep, for each ward, we sample a workplace size from a workplace size distribution, create aworkplace of this capacity and place it uniformly-at-random in that ward. We then randomlyassign individuals who work in that ward to this workplace. Similar to assignment of schools,we continue to create workplaces in this ward until every individual working in that wardgets assigned to a workplace, and we repeat this procedure for all wards. For Bengaluru, theOD matrix is obtained from the regional travel model used for Bengaluru. For Mumbai, basedon the “zone to zone” travel data from [21], an origin-destination matrix was extrapolatedbased on the population of each ward.The above assignments could be improved further in later versions of this simulator. Community spaces : Community spaces include day care centres, clinics, hospitals, shops,markets, banks, movie halls, marriage halls, malls, eateries, food messes, dining areas andrestaurants, public transit entities like bus stops, metro stops, bus terminals, train stations,airports, etc. While we hope to return to model a few of the important ones explicitly at alater time, we proceed along the route taken by [22] with two modifications.In our current implementation, each individual sees one community that is personalisedto the individual’s location and age and one transport space personalised to the individual’scommute distance. For ease of implementation, the personalisation of the community spaceis based on ward-level common local communities and a distance-kernel based weighting.The personalisation of the transport space is based on commute distance. Details are givenin Section IV-C.
Age-stratified interaction : The interactions across these communities could be age-stratified. This may be informed by social networks studies, for e.g., as in [23] which has been usedin a recent compartmentalised SEIR model [24].
Smaller subnetworks : We create smaller subnetworks in workplaces, schools and communi-ties, and associate certain number people to these smaller networks with the interpretation thatpeople in a smaller subnetwork have high contact rate among them compared to the others. Insome more detail, we create “project” networks at each workplace consisting of people in thatworkplace having closer interaction, a “class” network in each school consisting of studentsof the same age, a random community network among people in a given ward to model dailyrandom interactions, and a neighbourhood subnetwork among people living in a m × m square . These subnetworks are later used for identifying and testing/quarantining individualsbased on a contact tracing protocol.The output of all the above is our synthetic city on which infection spreads. Figure 42provides an indication of how close our synthetic city is to the true city in terms of theindicated statistics. B. Disease progression
We have used a simplified model of COVID-19 progression, based on descriptions in [25]and [8]. This will need updating as we get India specific data.An individual may have one of the following states, see Figure 43: susceptible, exposed,infective (pre-symptomatic or asymptomatic), recovered, symptomatic, hospitalised, critical,or deceased.We assume that initially the entire population is susceptible to the infection. Let τ denotethe time at which an individual is exposed to the virus, see Figure 43. The incubation periodis random with the Gamma distribution of shape 2 and scale 2.29; the mean incubationperiod is then 4.58 days (4.6 days in [8] and 4.58 in [26]). Individuals are infectiousfor an exponentially distributed period of mean duration 0.5 of a day. This covers bothpresymptomatic transmission and possible asymptomatic transmission. We assume that athird of the patients recover, these are the asymptomatic patients; the remaining two-thirddevelop symptoms. Estimates of the number of asymptomatic patients vary from 0.2 to 0.6.Though we have explored other asymptomatic fractions, we restrict attention here to 1/3.Symptomatic patients are assumed to be 1.5 times more infectious during the symptomaticperiod than during the pre-symptomatic but infective stage. Individuals either recover or move This dimension m comes from an approximate “squaring of a circle” of m radius (a) Bengaluru – Age distribution (b) Bengaluru – Household size distribution(c) Bengaluru – School size distribution (d) Bengaluru – Workplace size distribution(e) Bengaluru – Commuter distance distribution (f) Mumbai – Age distribution(g) Mumbai – Household size distribution (h) Mumbai – School size distribution(i) Mumbai – Workplace size distribution (j) Mumbai – Commuter distance distribution Fig. 42:
Validation of our synthetic Bengaluru and Mumbai. Figures 42(a)–42(e) show the validation plotsfor Bengaluru and Figures 42(f)–42(j) show the validation plots for Mumbai. Fig. 43:
A simplified model of COVID-19 progression. to the hospital after a random duration that is exponentially distributed with a mean of 5days . The probability that an individual recovers depends on the individual’s age . It isalso assumed that recovered individuals are no longer infective nor susceptible to a secondinfection. While hospitalised individuals may continue to be infectious, they are assumed tobe sufficiently isolated, and hence do not further contribute to the spread of the infection.Further progression of hospitalised individuals to critical care is mainly for assessing theneed for hospital beds, intensive care unit (ICU) beds, critical care equipments, etc. This willneed to be adapted to our local hospital protocol.Let us reiterate. Once a susceptible individual has been exposed, the trajectory in Figure 43takes over for that individual. Further progressions are (in our current implementation) onlybased on the agent’s age. C. Disease spread
At each time t , an infection rate λ n ( t ) is computed for each individual n based on theprevailing conditions. In the time duration ∆ t following time t , each susceptible individualmoves to the exposed state with probability − exp {− λ n ( t ) · ∆ t } , independently of all otherevents. Other transitions are as per the disease progression described earlier. Time is thenupdated to t + ∆ t , the conditions are then updated to reflect the new exposures, changes toinfectiousness, hospitalisations, recoveries, contact tracing, quarantines, tests, test outcomes,etc., during the period t to t + ∆ t . The process outlined at the beginning of this paragraph This needs to be updated based on hospitalisation guidelines. It is possible to add comorbidities - diabetes, hypertension, etc. – in addition to age. Mortality and prognosis appear todepend heavily on comorbidities. We leave it for the future. TABLE VI: Hospitalisation estimates taken from [8], based on studies in [25].
Age-group % symptomatic cases % hospitalised cases % critical cases(years) requiring hospitalisation requiring critical care deceased0 to 9 0.1% 5.0% 40%10 to 19 0.3% 5.0% 40%20 to 29 1.2% 5.0% 50%30 to 39 3.2% 05.0% 50%40 to 49 4.9% 6.3% 50%50 to 59 10.2% 12.2% 50%60 to 69 16.6% 27.4% 50%70 to 79 24.3% 43.2% 50%80+ 27.3% 70.9% 50% is repeated until the end of the simulation. ∆ t was taken to be 6 hours in our simulator andis configurable.A city of N individuals, H households, S schools, W workplaces, one community space(comprising C wards), one transport space, and associations of individuals to these entitiesis the starting point for the infection spread simulator. Infection spread is then implementedas follows.An individual n can transmit the virus in the infective (pre-symptomatic or asymptomaticstage) or in the symptomatic stage. At time t , this is indicated as I n ( t ) = 1 when infectiveand otherwise I n ( t ) = 0 otherwise.Additionally, each individual has two other parameters: a severity variable C n and a relativeinfectiousness variable ρ n , see [22]. Both bring in heterogeneity to the model. Severity C n = 1 if the individual suffers from a severe infection and C n = 0 otherwise; this is sampled at50% probability independently of all other events. Infectiousness ρ n is a random variable thatis Gamma distributed with shape 0.25 and scale 4 (so the mean is 1). The severity variablecaptures severity-related absenteeism at school/workplace, associated decrease of infectionspread at school/workplace, and the increase of infection spread at home.If the individual gets exposed at time τ n , a relative infection-stage-related infectiousnessis taken to be κ ( t − τ n ) at time t . For the disease progression described in the previoussection, this is 1 in the presymptomatic and asymptomatic stages, 1.5 in the symptomatic,hospitalised, and critical stages, and 0 in the other stages.To describe the infection spread at transport spaces, let T ( n ) = 1 if agent n uses publictransport and let T ( n ) = 0 otherwise. Let A n,t = 0 if at time t agent n is either (i) compliant and under quarantine, (ii) hospitalised, (iii) critical, or (iv) dead, and let A n,t = 1 if none ofthe above is true and agent n attends office at time t . We model the effectiveness of masksby reducing the ability of an infectious individual to transmit the infection by 20%, if a maskis worn (see [13]–[16]); let M n = 0 . if agent n wears a face mask in public transport and M n = 1 otherwise.Let β h , β s , β w , β T , β c , β ∗ h , β ∗ s , β ∗ w and β ∗ c denote the transmission coefficients at home,school, workplace, transport, community spaces, neighbourhood network, class network,project network and random community network, respectively. These can be viewed as scaledcontact rates with members in the household, school, workplace, community, neighbourhood,class, project and random community, respectively. More precisely, these are the expectednumber of eventful (infection spreading) contact opportunities in each of these interactionspaces. It accounts for the combined effect of frequency of meetings and the probability ofinfection spread during each meeting.For a susceptible individual, the rate of transmission is governed by the sum of productof contact rate β and infectiousness in all the interactions spaces. To model infectiousness,we consider three scenarios. Interactions without age-stratification : This is the simplest model where interactions withineach network is assumed to be homogeneous. A susceptible individual n (who belongs tohome h ( n ) , school s ( n ) , workplace w ( n ) , transport space T ( n ) , and community space c ( n ) )sees the following infection rate at time t : λ n ( t ) = (cid:88) n (cid:48) : h ( n (cid:48) )= h ( n ) n αh ( n ) · I n (cid:48) ( t ) β h κ ( t − τ n (cid:48) ) ρ n (cid:48) (1 + C n (cid:48) ( ω − (cid:88) n (cid:48) : s ( n (cid:48) )= s ( n ) n s ( n ) · I n (cid:48) ( t ) β s κ ( t − τ n (cid:48) ) ρ n (cid:48) (1 + C n (cid:48) ( ωψ s ( t − τ n ) − (cid:88) n (cid:48) : w ( n (cid:48) )= w ( n ) n w ( n ) · I n (cid:48) ( t ) β w κ ( t − τ n (cid:48) ) ρ n (cid:48) (1 + C n (cid:48) ( ωψ w ( t − τ n ) − (cid:80) n (cid:48) : T ( n (cid:48) )=1 A n (cid:48) ,t (cid:80) n (cid:48) T ( n (cid:48) ) × (cid:88) n (cid:48) : T ( n (cid:48) )= T ( n ) (cid:32) d n (cid:48) ,w ( n (cid:48) ) I n (cid:48) ( t ) β T M n (cid:48) (cid:80) n (cid:48) : T ( n (cid:48) )= T ( n ) d n (cid:48) ,w ( n (cid:48) ) (cid:33) + ζ ( a n ) · f ( d n,c ) (cid:80) c (cid:48) f ( d c,c (cid:48) ) (cid:88) c (cid:48) f ( d c,c (cid:48) ) h c,c (cid:48) ( t ) (1)where h c,c (cid:48) ( t ) = (cid:32) (cid:80) n (cid:48) : c ( n (cid:48) )= c (cid:48) f ( d n (cid:48) ,c ( n (cid:48) ) ) · ζ ( a n (cid:48) ) · I n (cid:48) ( t ) β c r c κ ( t − τ n (cid:48) ) ρ n (cid:48) (1 + C n (cid:48) ( ω − (cid:80) n (cid:48) f ( d n (cid:48) ,c ( n (cid:48) ) ) (cid:33) (2) The expression (1) can be viewed as the rate at which the susceptible individual n contractsthe infection at time t . Each of the components on the right-hand side indicates the rate fromhome, school, workplace, transport space, and community. The additional quantities, overand above what we have already described, are as follows.The parameter α determines how household transmission rate scales with household size,a crowding-at-household factor. It increases the propensity to spread the infection by a factor n − α . We have taken α = 0 . , see [22].A common parameter ω indicates how a severely infected person affects a susceptible one,as will be clear from below. (This is to be tuned at a later stage and is set to 2 now).The functions ψ s ( · ) and ψ w ( · ) account for absenteeism in case of a severe infection. Itcan be time-varying and can depend on school or workplace. We take ψ s ( t ) = 0 . and ψ w ( t ) = 0 . while infective and after one day since infectiousness. School-goers with severeinfection contribute lesser to the infection spread, due to higher absenteeism, than those thatgo to workplaces; moreover, the absenteeism results in an increased spreading rate at home.The function ζ ( a ) is the relative travel-related contact rate of an individual aged a . Wetake this to be 0.1, 0.25, 0.5, 0.75, 1, 1, 1, 1, 1, 1, 1, 1, 0.75, 0.5, 0.25, 0.1 for the variousage groups in steps of 5 years, with the last one being the 80+ category.The quantity h c,c (cid:48) ( t ) represents the transmission rate from individuals in ward c (cid:48) to anindividual in ward c . As above, each individual contributes in a distance-weighted way inhow an individual in a ward c (cid:48) affects another individual in another ward c .The factor r c stands for a high-density interaction multiplying factor. For Mumbai, r c = 2 for some high density areas and r c = 1 for the other areas. For Bengaluru r c = 1 for allwards.The function f ( · ) is a distance kernel that can be matched to the travel patterns in the city.Finally, our choice of the infection rate from the community space is a little different fromthe rate specified in [22], in order to enable an efficient implementation. When the distancekernel is f ( d ) = 1 / (1 + ( d/a ) b ) and d (cid:28) a , i.e., the wards are small, then our specificationis close to that indicated in [22]. We take a = 10 . km and b = 5 . , based on a fit ondata for Bengaluru.As one can see from (1), we have one community space but with contributions fromvarious wards. This enables inclusion of ‘containment zones’ and the associated restrictionof interaction across such zones, as we shall soon describe. Age-stratified interactions : If this is enabled, the home, school, workplace and communityinteraction rates have an extra factor M hn,n (cid:48) , M sn,n (cid:48) , and M wn,n (cid:48) in the summand which accounts for age-stratified interactions. Each of these depends on n and n (cid:48) only through the ages ofagents n and n (cid:48) . The resulting contact rate for individual n at time t is then: λ n ( t ) = (cid:88) n (cid:48) : h ( n (cid:48) )= h ( n ) M hn,n (cid:48) n αh ( n ) · I n (cid:48) ( t ) β h κ ( t − τ n (cid:48) ) ρ n (cid:48) (1 + C n (cid:48) ( ω − (cid:88) n (cid:48) : s ( n (cid:48) )= s ( n ) M sn,n (cid:48) n s ( n ) · I n (cid:48) ( t ) β s κ ( t − τ n (cid:48) ) ρ n (cid:48) (1 + C n (cid:48) ( ωψ s ( t − τ n ) − (cid:88) n (cid:48) : w ( n (cid:48) )= w ( n ) M wn,n (cid:48) n w ( n ) · I n (cid:48) ( t ) β w κ ( t − τ n (cid:48) ) ρ n (cid:48) (1 + C n (cid:48) ( ωψ w ( t − τ n ) − (cid:80) n (cid:48) : T ( n (cid:48) )=1 A n (cid:48) ,t (cid:80) n (cid:48) T ( n (cid:48) ) × (cid:88) n (cid:48) : T ( n (cid:48) )= T ( n ) (cid:32) d n (cid:48) ,w ( n (cid:48) ) I n (cid:48) ( t ) β T M n (cid:48) (cid:80) n (cid:48) : T ( n (cid:48) )= T ( n ) d n (cid:48) ,w ( n (cid:48) ) (cid:33) + ζ ( a n ) · f ( d n,c ) (cid:80) c (cid:48) f ( d c,c (cid:48) ) (cid:88) c (cid:48) f ( d c,c (cid:48) ) h c,c (cid:48) ( t ) (3)where h c,c (cid:48) ( t ) is given in (2). Computational complexity can be reduced by focusing only onthe principal components of M h , M s , and M w . Interactions with smaller subnetworks : In this situation, we have additional contact rateparameters, one for each smaller subnetwork: let β ∗ h , β ∗ s , β ∗ w and β ∗ c denote the transmissioncoefficients at neighbourhood network, class network, project network and random communitynetwork respectively. Then, an agent n (who belongs to neighbourhood network H ( n ) ,class S ( n ) , project W ( n ) and random community C ( n ) , in addition to home h ( n ) , school s ( n ) , workplace w ( n ) , transport space T ( n ) , and community space c ( n ) ) sees the following infection rate at time t : λ n ( t ) = (cid:88) n (cid:48) : h ( n (cid:48) )= h ( n ) n αh ( n ) · I n (cid:48) ( t ) β h κ ( t − τ n (cid:48) ) ρ n (cid:48) (1 + C n (cid:48) ( ω − ζ ( a n ) (cid:88) n (cid:48) : H ( n (cid:48) )= H ( n ) n H ( n ) · ζ ( a n (cid:48) ) I n (cid:48) ( t ) β ∗ h κ ( t − τ n (cid:48) ) ρ n (cid:48) (1 + C n (cid:48) ( ω − (larger neighbourhood interaction) + ζ ( a n ) f ( d n,c ( n ) ) (cid:80) n (cid:48) : C ( n (cid:48) )= C ( n ) f ( d n (cid:48) ,c ( n (cid:48) ) ) × (cid:88) n (cid:48) : C ( n (cid:48) )= C ( n ) f ( d n (cid:48) ,c ( n (cid:48) ) ) ζ ( a n (cid:48) ) I n (cid:48) ( t ) β ∗ c κ ( t − τ n (cid:48) ) ρ n (cid:48) (1 + C n (cid:48) ( ω − (close friends’ circle interaction) + (cid:88) n (cid:48) : s ( n (cid:48) )= s ( n ) n s ( n ) · I n (cid:48) ( t ) β s κ ( t − τ n (cid:48) ) ρ n (cid:48) (1 + C n (cid:48) ( ωψ s ( t − τ n ) − (cid:88) n (cid:48) : S ( n (cid:48) )= S ( n ) n S ( n ) · I n (cid:48) ( t ) β ∗ s κ ( t − τ n (cid:48) ) ρ n (cid:48) (1 + C n (cid:48) ( ωψ s ( t − τ n ) − (class network interaction) + (cid:88) n (cid:48) : w ( n (cid:48) )= w ( n ) n w ( n ) · I n (cid:48) ( t ) β w κ ( t − τ n (cid:48) ) ρ n (cid:48) (1 + C n (cid:48) ( ωψ w ( t − τ n ) − (cid:88) n (cid:48) : W ( n (cid:48) )= W ( n ) n W ( n ) · I n (cid:48) ( t ) β ∗ w κ ( t − τ n (cid:48) ) ρ n (cid:48) (1 + C n (cid:48) ( ωψ w ( t − τ n ) − (project network interaction) + (cid:80) n (cid:48) : T ( n (cid:48) )=1 A n (cid:48) ,t (cid:80) n (cid:48) T ( n (cid:48) ) × (cid:88) n (cid:48) : T ( n (cid:48) )= T ( n ) (cid:32) d n (cid:48) ,w ( n (cid:48) ) I n (cid:48) ( t ) β T M n (cid:48) (cid:80) n (cid:48) : T ( n (cid:48) )= T ( n ) d n (cid:48) ,w ( n (cid:48) ) (cid:33) + ζ ( a n ) · f ( d n,c ) (cid:80) c (cid:48) f ( d c,c (cid:48) ) (cid:88) c (cid:48) f ( d c,c (cid:48) ) h c,c (cid:48) ( t ) (4)where h c,c (cid:48) ( t ) is given in (2). The subnetwork interactions are stronger contexts for diseasespread. Contact tracing targets exactly these subnetworks for additional testing, case isolationor quarantine. D. Seeding of infection
Two methods of seeding the infection have been implemented. • A small number of individuals can be set to either exposed, presymptomatic/asymptomatic,or symptomatic states, at time t = 0 , to seed the infection. This can be done randomlybased either on ward-level probabilities, which could be input to the simulator, or it canbe done uniformly at random across all wards in the city. • A seeding file indicates the average number of individuals who should be seeded on eachday in the first stage of infectiousness (presymptomatic or asymptomatic). This couldbe done based on data for patients with a foreign travel history who eventually visiteda hospital. A certain multiplication factor then accounts for the asymptomatic and thesymptomatic individuals that recover without the need to visit the hospital. The seedingis done at a random time earlier in the time line, based on the disease progression.
E. Calibration
We calibrate our model by tuning the transmission coefficients at various interaction spacesunder the no-intervention scenario in order to match the cumulative fatalities to a targetcurve. We assume a common upscaling factor ˜ β for the transmission coefficients of smallersubnetworks, i.e., we set β ∗ w = ˜ ββ w , β ∗ s = ˜ ββ s and β ∗ h = β ∗ c = ˜ ββ c . We assume that ˜ β = 9 , indicating that the subnetworks account for 90% of the overall contacts. The followingheuristic iterative algorithm inspired by stochastic approximation is then used to identify thebest choice of the free parameters. β h ( n + 1) = (cid:18) β h ( n ) − Λ h ( n ) n + 3 (cid:19) × [exp( m ∗ − m ( n ))] /aa ,β w ( n + 1) = (cid:18) β w ( n ) − Λ w ( n ) n + 3 (cid:19) × [exp( m ∗ − m ( n ))] /aa ,β c ( n + 1) = (cid:18) β c ( n ) − Λ c ( n ) n + 3 (cid:19) × [exp( m ∗ − m ( n ))] /aa , where [exp( m ∗ − m ( n ))] /aa = min { max { exp( m ∗ − m ( n )) , a } , /a } , Λ h ( n ) (resp. Λ w ( n ) , Λ c ( n ) ) is the fraction of infections from home (resp. workplace, community) in the n thstep, and m ( n ) is the slope of the cumulative fatalities curve in log-scale in an initial linearregion, obtained by running the simulator on a smaller city file (of 1 million population) inthe no intervention scenario. We set a = 2 / . To minimise the effect of stochasticity fromthe simulator, in each step n , we run the simulator times and take the average values of Λ h ( n ) , Λ w ( n ) , Λ c ( n ) and m ( n ) . We stop the algorithm at time n if we meet our targets, i.e.,if | m ( n ) − m ∗ | ≤ . , | Λ h ( n ) − Λ ∗ h | ≤ . , | Λ w ( n ) − Λ ∗ w | ≤ . , and | Λ c ( n ) − Λ ∗ c | ≤ . , where Λ ∗ h = Λ ∗ w = Λ ∗ c = 1 / , and m ∗ is the target slope (the target slope is similarlycomputed from the cumulative fatalities data in log scale; for example, the India fatalitiescurve in the range 130-199 gives a slope of m ∗ = 0 . ). Once the slopes are matched,assuming that the simulator starts on 01 March 2020, we find the delay between the fatalitiescurve from the simulator and the target data. We then use the resulting contact rates and theabove calibration delay to launch our simulations.To avoid any oscillatory behaviour of the calibration algorithm, we also set the scale factorin each of the above update steps to be [exp(( m ∗ − m ( n )) /n )] /aa whenever | Λ h ( n ) − Λ ∗ h | ≤ . , | Λ w ( n ) − Λ ∗ w | ≤ . and | Λ c ( n ) − Λ ∗ c | ≤ . . In addition, we set the scale factor tobe [exp(( m ∗ − m ( n )) / ( n − /aa if n ≥ .For the simulation results presented in the case studies, we identified the m ∗ as follows. Weassumed a counterfactual situation where the national level of infection, up to the date whenthe lockdown’s effect is not yet likely to have been seen, estimated to be 8–10 April 2020,is moved to the city under study. There were 199 fatalities in India up to 10 April 2020. TheIndia cases and fatalities data is based on daily updates compiled by the European Centre forDisease Prevention and Control [27]. The counterfactual situation (all of India’s infectionsin the isolated city under study) is to ensure that sufficient data is available for calibrationbefore the national lockdown’s effect is encountered. The fatalities up to this date were likelydue to contacts prior to the start of the lockdown. The slope of this curve (in the log-domain)gives the m ∗ . The calibration is further done on a smaller version of the city, with 10 lakhpopulation. The resulting parameters are then used on the full-scale city.We do not calibrate β T , the transmission coefficient at transport space. For the calibra-tion step we take this parameter to be zero while tuning the other parameters. A heuristicjustification is as follows. Bengaluru travel interactions will likely be captured through thelocal community interactions, and we keep it zero throughout, even in the case studies. ForMumbai however, local trains are a key mode of daily transportation with a population ofthe order of 75 lakh travelling daily using this mode in normal times. However, trains werestopped in Mumbai prior to the national lockdown and were running below capacity for atleast a week before that. Moreover, the initial infections were seeded by travellers that camefrom abroad. The primary mode of travel for this group is unlikely to be rail transport. Sowe disabled the transport space while calibrating by setting β T = 0 . Subsequently for thetrains on/off case study, we used a heuristic calculation of β T ; see [28, Section IV].The above procedures identify the contact-related parameters. Other parameters are thedistance kernel parameters, the parameter α that accounts for crowding in households, the age- stratified interactions, the distribution parameters for individual infectiousness, the probabilityof severity, etc. These are set as follows:TABLE VII: Model parameters Parameter Symbol Bengaluru MumbaiTransmission coefficient at home β h β s β w β c ˜ β β t − α r c f ( d ) = 1 / (1 + ( d/a ) b ) ( a, b ) (10 . , . . , . Infectiousness shape (Gamma distributed) (shape,scale) (0 . ,
4) (0 . , Severity probability Pr { C n = 1 } M n,n (cid:48) Not used Not usedProject subnetwork size range n W ( n ) −
10 3 − Family friends’ subnetwork range no symbol 2-5 families 2-5 families
F. Interventions
The simulator has the capability to accommodate interventions and compliance. Table VIIIdescribes some of the interventions in [8], some adapted to suit our demographics, andsome new interventions involving the nation-wide 40-day ‘lockdown’ in India and variousscenarios of ‘unlock’. These are fairly straightforward to implement – we modulate anindividual’s contact rate with an interaction space (both into the interaction space and outof the interaction space) by a suitable factor associated with intervention. For example, onecould easily implement and study cyclic exit strategies as done in [29]. The triggers for cycliccontrols could be based on signals such as the number of individuals that are hospitalised,as done in our soft ward containment. Yet another one is to quarantine or case isolate basedon contact tracing, as we will describe next.
G. Contact tracing
Our simulator also includes a framework to study the impact of early contact tracingand testing. We assume that contacts of an individual in the smaller networks such asneighbourhood network, project network, class network and random community network TABLE VIII: Interventions.
Label Policy DescriptionCI Case isolation at home Symptomatic individuals stay at home for 7 days, non-household contactsreduced by 90% during this period, household contacts reduce by 25%.HQ Voluntary home quarantine Once a symptomatic individual has been identified, all members of thehousehold remain at home for 14 days. Non-household contacts reducedby 90% during this period, household contacts reduce by 25%.SDO Social distancing of thoseaged 65 and over Non-household contacts reduce by 75%.LD Lockdown Closure of schools and colleges. Only essential workplaces active. For acompliant household, household contact rate doubles, community contactrate reduces by 75%, workspace contact rate reduces by 75%. For a non-compliant household, household contact rate increases by 25%, workspacecontact rate reduces by 75%, and no change to community contact rate.LD40-CI Lockdown for 40 days Lockdown for 40 days and then normal activity, but with CI.LD40-PE-CI One particular phased emer-gence (PE) from lockdown Lockdown for 40 days, then CI, HQ and SDO for 14 days. Schools andcolleges remain closed during this period. Normal activity resumes afterthis period with reopening of schools and colleges, but with CI.LD40-PE-SCCI Another phased emergencefrom lockdown Lockdown for 40 days, then CI, HQ and SDO for 14 days. Schools andcolleges remain closed during this period (SC). Normal activity resumesafter this period but schools and colleges remain closed for another 28days (SC). CI remains in place throughout.LD40-PEOE-CI A third type of phased emer-gence from lockdown Lockdown for 40 days, then CI, HQ and SDO for 14 days. Schools andcolleges remain closed and an odd-even workplace strategy is in placeduring this period. Normal activity resumes after this period. CI remainsin force throughout. can be identified and tested/quarantined. The current contact tracing protocol quarantinescertain primary contacts and tests a subset of these (e.g., symptomatic primary contacts). Inour implementation, based on our study of ICMR’s testing protocol, given an index case, allhousehold members, a fraction of the friends circle, a fraction of the inner school/workplacecircle, and a fraction of the neighbourhood community are termed as primary contacts ofthis index case. All of these are quarantined, and a fraction of the symptomatic and anotherfraction of the asymptomatic among these are tested. Those who test positive become newindex cases and spawn further contact tracing. The testing fractions are calibrated to matchthe actual reported cases and the test-positivity rate. H. Limitations
We list some limitations of our simulator. • We do not have activity modelling in our simulator. As a consequence, weekly anddaily patterns on interactions are not taken into account; for instance, the absence ofinteraction in workplaces and schools during weekends/public holidays, an increasedinteraction in public transport during morning and evening peak hours etc. are not takeninto account in our model. Instead, all these factors are abstracted into a single infectionrate for each individual prescribed by (1), (3) and (4). • Some of the data that we need in our simulator, such as the household size distribution,workplace size distribution, school size distribution, commuter distance distribution etc.,can perhaps be difficult to obtain for some cities. • We have too many free parameters in our model. This can lead to overfitting resultingin high generalisation error. • The framework is computationally intensive. • Since the disease spread model has quite a bit of stochasticity (e.g., the incubation time),we need to perform multiple runs of our simulator and take an average of the outputs.We do not have an estimate on the variability of our outputs across multiple runs; suchan analysis will be essential to determine the number of runs we need to perform inorder for our outputs to be close to the average.V. A
LGORITHMIC ASPECTS
A. Algorithmic aspects related to city generation
Generation of a synthetic city is performed via the following steps.1)
Data gathering and data preparation involves the following.(a) Census Data Processing: The primary data sources used to generate the syntheticcity are the 2011 decennial census data of India and the intermediate survey reportsfor a city. The raw data are typically either in spreadsheets or as tables in a PDFdocument. We use Python packages like pandas and tabula to clean, process andprepare the data required for creating a synthetic city.The data required for creating a synthetic city like the ward-wise demograph-ics, employment status, number of households and the origin-destination matrixare created as separate comma separated values (csv) files. Distributions like thehousehold size, workplace size, school size, for the city are collected as a singleJavaScript Object Notation (JSON) file. (b) Geo-spatial mapping : In addition to the census data, the instantiation for the cityalso requires the geographic representations for a ward like the ward centre andward boundaries. These are obtained from map files. Map files are mined indifferent formats like shapefiles (.shp, .shx) or geoJSON (.geojson), which areprocessed using Python‘s geopandas package.2)
Instantiating the city files is done by running a python script on the following inputs:the map data (.geojson), the census data on the demographics(.csv), households(.csv)and employment(.csv) files along with the additional parameters specified in ‘cityPro-file.json’. The instantiation of a synthetic city is done in three stages namely:(a)
Processing Inputs : The script ingests the input (.csv) files using the pandas packageand computes parameters based on the input like the unemployment fraction,fraction of population in each ward. The GeoJSON file is processed with thegeopandas package to parse the input file and the shapely package to computethe ward centre, the ward boundaries and the neighbouring wards. Apart fromthe data files, the target population for which the instantiation is to be done, theaverage number of students in a school, the average number of individuals inone workplace are input parameters specified at the start of the script. The agedistribution, household-size distribution and school-size distribution are taken asinputs from the ‘cityProfile.json’ file.(b)
Instantiating individuals comprises of an algorithm that randomly assigns individ-uals to households by respecting the household-size distribution. Each householdhas individuals assigned with generational gaps, yet the instantiated population’sempirical age distribution must match the given age distribution. Individuals areassigned to workplaces or schools or neither, based on their age and the unemployedfraction, and are assigned the appropriate ‘workplaceType’. Once an individual isassigned to a household, the location of the individual is mapped to the location ofthe assigned household. While instantiating households, the ward number to whichthe household is assigned is specified and based on the ward number the respectiveward boundaries are obtained from the map data in the GeoJSON file. The wardboundaries are typically represented as ‘Polygons’. The location of households ,workplaces and schools are randomly sampled as a point inside the ward boundary.For instantiating households in high-density areas, we sample locations either froma GeoJSON file with boundaries of the high-density areas or from a collection of pre-sampled locations of households in high density areas. Common areas wherecommunity interactions take place are instantiated at the ward centres, assumed tobe the centroids of the polygons. These tasks are accomplished using the followingpython packages: numpy, random, pandas and shapely. The outputs of this stageare collections of the instantiated individuals, their assigned households, schools,workplaces, transport and community areas.(c) Additional processing for generating city files : Before generating the city files,additional processing is done on the dataframes which includes computing thedistance of the individuals to their respective ward centres. This stage uses thepandas package for processing and generating the city files in the JSON file formatfor each instantiated collection namely the individuals, households, workplaces,schools, community centres, and distance between wards.
B. Algorithmic aspects related to disease spread
The disease progression part of the simulator is broadly implemented as follows. Thereare four time steps on a given day. At each time step, we go through each susceptible agentand find out the infection rate given by either (1), (3) or (4) depending on the interaction thatwe want to model. We then update the disease progression status of that agent based on theinfection rate. Once an individual becomes exposed, this person goes through various stagesof the disease depending on age, and contributes to the infection rate of other individuals inthe individual’s interaction space as long as the individual is infectious. Eventually, the agentrecovers from the disease or dies. At the end of the simulation, we output a time series ofvarious quantities of interest into a file, such as the daily number of cases, cumulative numberof cases, daily number of hospitalisations, daily number of fatalities, cumulative number offatalities, etc.Some of the key features of our simulator that help reduce the space and time complexityare as follows. • We have a single community space per ward where individuals living in that wardcome together and interact. We then have an interaction among communities to modelcommunity interactions among people living in different wards. With n agents and c communities, such a model keeps the computational complexity at O ( n ) + O ( c ) . If wehad considered a more complex interaction between individuals, where each individualinteracts with every other individual living in the city with a certain contact rate, thecomplexity would have been O ( n ) . Modelling of other interaction spaces such as households, schools, workplaces and transport spaces also results in a similar reductionin time complexity from O ( n ) to O ( n ) . Since the number of agents are typically of theorder of , such a reduction has a huge impact on the running time of the simulator. • Contact tracing requires us to maintain a list of contacts made by each agent. In ourimplementation, we assume that each individual has a certain number of contacts thatwe can trace (which is random, but independent of n ). As a result, the space complexitybecomes O ( n ) instead of O ( n ) . • In the age-stratified interaction as well as OD-matrix based distance kernel, we considerdominant terms of the age-based contact rate matrix as well as OD-matrix by doinga principal component analysis and by focusing on a few important components. Thishelps simplify the summations in (3).These optimisation features appear to be novel features of our simulator.VI. C
ONCLUSION
In this work, we built an agent-based simulator to study the impact of various non-pharmaceutical interventions in the context of the ongoing COVID-19 pandemic. We demon-strated the capabilities of our simulator via various case studies for Bengaluru and Mumbai.Some of the key features of our simulator include age-stratified interaction that capturesheterogeneity in interaction among people in a given interaction space, the ability to imple-ment various interventions such as soft ward containment, phased opening of workplaces andcommunity spaces, a broad class of contact tracing based testing and case isolation protocols,etc. These features help our simulator to capture the ground reality very well and provideus with realistic predictions. Some future directions include bringing in movement of peopleinto and out of the city and studying the impact of various mobility patterns, modelling andstudying the impact on public-health oriented decisions on the economy, incorporating activitymodelling into our simulator and using the simulator to obtain district-scale or country-scalepredictions. We hope that such agent-based simulators find a regular place in every publichealth official’s tool kit. A
CKNOWLEDGMENTS
We sincerely thank Arpit Agarwal, Priyanka Agrawal, Bharadwaj Amrutur, M. S. Ashwin,Siva Athreya, Abhijit Awadhiya, Chiranjib Bhattacharyya, Vijay Chandru, Avhishek Chat-terjee, Arpan Chattopadhyay, Siddhartha Gadgil, Aditya Gopalan, K. V. S. Hari, RameshHariharan, Aniruddha Iyer, Srikanth Iyer, Shipra Jain, Subhasis Jethy, Jacob John, Shruti Kakade, Navin Kashyap, Micky Kedia, DataMeet (a community of Data Science and OpenData enthusiasts), Revanth Krishna, Vrishab Krishna, Manjunath Krishnapur, Anurag Kumar,Rahul Lodhe, Rahul Madhavan, Madhav Marathe, Satyajit Mayor, Gautam Menon, ShirazMinwalla, Prem Mony, Chandra Murthy, Y. Narahari, Uma Chandra Mouli Natchu, PraneethNetrapalli, Abdul Pinjari, Vinod Prabhakaran, Dr. Prabhu, Rishi Prajapati, Ketan Rajawat,G. Rangarajan, G. V. Sagar, Agrim Sharma, Abhishek Sinha, Mukund Thattai, HimanshuTyagi, Srinivasan Venkataramanan, V. Vinay, Anil Vullikanti, and many volunteers for theirvaluable comments and help.The SahasraT supercomputing cluster at the Supercomputer Education and Research Centre(SERC), Indian Institute of Science, was used for most of the simulations.R
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