Assessing the Interplay between travel patterns and SARS-CoV-2 outbreak in realistic urban setting
Rohan Patil, Raviraj Dave, Harsh Patel, Viraj M Shah, Deep Chakrabarti, Udit Bhatia
PPatil et al.
RESEARCH
Assessing the Interplay between travel patternsand SARS-CoV-2 outbreak in realistic urbansetting
Rohan Patil † , Raviraj Dave † , Harsh Patel , Viraj M. Shah , Deep Chakrabarti and Udit Bhatia * Correspondence:[email protected] Discipline of Computer Scienceand Engineering, Indian Instituteof Technology, Gandhinagar, IndiaFull list of author information isavailable at the end of the article † Equal contributors
AbstractBackground:
The dense social contact networks and high mobility in congestedurban areas facilitate the rapid transmission of infectious diseases. Typicalmechanistic epidemiological models are either based on uniform mixing withad-hoc contact processes or need real-time or archived population mobility datato simulate the social networks. However, the rapid and global transmission ofthe novel coronavirus (SARS-CoV-2) has led to unprecedented lockdowns atglobal and regional scales, leaving the archived datasets to limited use.
Findings:
While it is often hypothesized that population density is a significantdriver in disease propagation, the disparate disease trajectories and infection ratesexhibited by the different cities with comparable densities require ahigh-resolution description of the disease and its drivers. In this study, we explorethe impact of creation of containment zones on travel patterns within the city.Further, we use a dynamical network-based infectious disease model tounderstand the key drivers of disease spread at sub-kilometer scales demonstratedin the city of Ahmedabad, India, which has been classified as a SARS-CoV-2hotspot. We find that in addition to the contact network and population density,road connectivity patterns and ease of transit are strongly correlated with therate of transmission of the disease. Given the limited access to real-time trafficdata during lockdowns, we generate road connectivity networks using open-sourceimageries and travel patterns from open-source surveys and government reports.Within the proposed framework, we then analyze the relative merits of socialdistancing, enforced lockdowns, and enhanced testing and quarantiningmitigating the disease spread.
Scope:
Our results suggest that the declaration of micro-containment zoneswithin the city with high road network density combined with enhanced testingcan help in containing the outbreaks until clinical interventions become available.
Keywords:
Transportation Network; SARS CoV2; Social Networks;Transportation Gravity Models
Introduction
Modern history is witness to several infectious disease pandemics which have shapedour knowledge of their epidemiology, transmission, and management [1]. In the past200 years, at least four strains of influenza, seven waves of cholera, tuberculosis, andthe human immunodeficiency virus (HIV) have accounted for the deaths of nearly100 million people [2, 3]. Mathematical modelling of infectious diseases allows usto predict an epidemic accurately, recognize uncertainties, and quantify situations a r X i v : . [ phy s i c s . s o c - ph ] S e p atil et al. Page 2 of 19 to identify possible worst-case situations that can guide public health planning anddecision making [4, 5].Classically, mathematical models of infectious diseases were dependent on theclassification of individuals on their epidemiological status based on their poten-tial ability to host and transmit a pathogen: Susceptible, Infectious, and Recovered[SIR] [6, 7, 8]. The SIR model is the most fundamental epidemiological model thatrelies on calculating the proportional burden of each of these three classes, and thetransitions between them. In the context of an epidemic, assuming no births ordeaths in a population, the only two possible transitions are infection (movementfrom susceptible to infected) and recovery (movement from infected to remission).For the sake of simplicity, it can be assumed that the susceptibility is proportionalto the prevalence of infection or the disease burden in the community, and recov-eries occur at a constant rate [9]. Estimating transmission and recovery, the epi-demic progresses exponentially until the growth rate slows and the epidemic curveplateaus; following which eventually over time the epidemic cannot be sustained andis eradicated [6]. A failing of the traditional SIR model is its inability to accountfor spatial aspects of disease spread. The 2001 dynamics of foot and mouth diseasein the United Kingdom were demonstrated by explicit individualised modelling astransmission between farms that would not have been possible by traditional SIRmodels alone. Such models pointed at localised depletion of susceptible contacts asthe mechanism for the slowing of the epidemic [6, 10]. The HIV pandemic is charac-terised by a chronic infective state. The transmission of such a sexually transmittedinfection is dependent on the host immune status, the infected individual’s viralload, and multiple social aspects like sexual practices of interactions between multi-ple structured risk groups within the population. In such a situation, the variabilityin infectious state predicts the progression of the epidemic and stochasticity meritsmore complex modelling [11]. Similarly, pandemics of influenza or flu-like illnessescan be accounted for by age and risk-structured models, which are explained bydistinct risk groups for infection and fatality (age, health care workers, comorbidconditions), and the inherent nature of people to preferentially socialise with othersof a similar age—a principle known as assortativity [7, 12]. More complex modellingfocuses on the individual as a unit of the population describing individual interac-tions of each person in a population, in contrast to estimating the proportions ofpeople with a certain disease status. The shift from a population-based model toan individual-based model is a powerful tool that helps to account for complexbiologically and socially relevant interactions [13, 14].Reliability of projections from individual based epidemiological model criticallydepends upon the realistic estimates of human mobility, which is often simulatedusing suite of agent-based simulations, network science approaches, and data sciencemethods [15, 16, 17]. For example, Eubank et al. (2004) demonstrated the applica-bility of highly resolved agent based simulation tools that combine census and landuse data with parameterized models to simulate the progression of infectious diseasein realistic urban social networks [15]. Balcan et al. (2009) analyzed mobility datafrom various countries around the world and integrated in a worldwide structuredmeta-population mechanistic epidemic model to understand the role of infection dueto multi-scale dynamic processes [18]. Ajelli et al.(2010) noted a good agreement atil et al.
Page 3 of 19 between highly detailed agent-based modeling approaches and spatially structuredmechanistic meta-population models. However, researchers note that while mobilitynetworks used in meta-population models provide an accurate description of spread-ing phenomenon, detailed estimates of the impact at finer scales is hampered by thethe low level of detail contained in such modeling schemes. On other hand, whileagent-based modeling approaches are highly detailed, gathering high confidence de-tailed datasets, specifically in heterogeneous regions across the world, is a challenge[19]. In the context of vector borne epidemics such as Zika virus (ZIKV) epidemic,researchers have integrated the high spatial and temporal resolution real-world de-mographic, mobility, socioeconomic and climatic condition datasets to estimate theprofiles of ZIKV infections [17]. In other studies, researchers have combined thestate-space models such as population based Suspected (S), Exposed (E), Infected(I), and Recovery (R) or SEIR models in combination with Google Trend datasetsto understand the evolution of Flu trends in the United States [20]. SARS-CoV-2epidemic spread across the Globe in early 2020, mathematical, statistical and ma-chine learning based models gained prominence to find out how to slow and or stopthe spread [21, 22, 23, 24] . Moreover, researchers referred to the ongoing effortsto model the spread of SARS-CoV2 as ”war time”research where scientists have todeal with limited data, multiple assumptions and changing landscapes [24]. We notethat despite the structural, mathematical and procedural differences which exist inthe wide spectrum of epidemic models, realistic representation of human mobilitypatterns, and social interactions play a key role in governing model performance tounderstand the disease progression.To model human mobility, travel demand models and activity based models aretypically used. While travel demand models focus on estimating aggregate road us-age in long run using aggregated zonal statistics often obtained from census andhousehold surveys. More recent methods try to learn about human behavior in urbanareas by using data collected from location-aware technologies including telecommu-nication activity datasets and Global Position System data archives [25].We notethat while massive and passive cellphone data can effectively generate completeurban mobility patterns [26], these datasets are typically non-open source givenprivacy and security concerns. In absence of high resolution activity data, simpli-fied models of human mobility such as gravity models are often used to understandthe spreading of viruses and the evolution of epidemics [19, 27, 28].The novel Coronavirus (2019-nCoV) first identified in Wuhan, China has spreadto 213 countries as of August 2020 with more than 24 Million confirmed casesreported worldwide [29]. While much still needs to be learnt about the virus, itsclinical characteristics, extent of inter-human transmission , and the spectrum ofclinical disease, it is established that transmission of SARS-CoV-2 occurred to greatextent through superspreading events [30]. While accurate forecasting of spread aswell as number of deaths and recoveries require ample historical data, contact net-works, and identification of zeroth case in different regions in addition to the clinicalparameters [31]. While multiple modeling groups across the globes have proactivelyfocused on modeling the spread at global and regional scales [32, 24, 22], studiesat urban and city scales are limited [33, 34]. Given the diversity in socioeconomicfactors, spread characteristics, demographics, healthcare facilities, management of atil et al.
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Region of Study and Data
We use Ahmedabad Municipal Corporation (AMC) as the study region (Figure1). Ahmedabad city has a population of 5.6 million (Census 2011), making it thefifth-highest populous city in India. The city’s geographical location is 23.0225 N,72.5714 atil et al. Page 5 of 19 an open-source repository that compiles the patient data from various governmentsources in near-real time [42].
Methods and Materials
Geo-spatial boundary and Population assignment
We converted the road network into an undirected network graph, which translatesthe road’s geometries into nodes and links. The attributes extracted from the dataare the nodes’ location, length of links, categories of links, and the links’ end coor-dinates. The travel time of the road section is a crucial parameter to understand thebehavior of traffic. We integrated travel time considering the category and lengthof a road section.To define the transportation network boundary in AMC, we used the AMC bound-ary geo-spatial data and extracted the modeled population data for the same (Figure3(a)). To include the incoming and outgoing traffic from the city’s outskirts, we gen-erated a buffer radius of 1km. We considered the incoming traffic on the boundaryjunction of the city network (Figure 3(c)). Then the whole boundary of the city issplit into a unique region of the Voronoi cell (Figure 3(d)). Then we estimated thepopulation intersecting with each unique cell (Equation 1). Each cell populationdata is transferred to their respective road junctions. P i = Σ P t × Area ( C i × C t ) Area C t (1)where: • P i = Population in each Voronoi polygon • P t = Modeled population • C i = Cell of Voronoi polygon • C t = Cell of populationWe also incorporated the land use (Figure 3(b)) into the analysis to create realtraffic congestion scenarios for post-lock down situations in the city. The assumptionis made that around 1/4 th of the population will commute from residential to com-mercial for daily work, making the industrial and commercial area more crowdedcompared to the residential area. The re-allocation of population assignment indi-cates the highly congested pockets in the city. Traffic demand forecasting model
The transportation model enables travel demand forecast while taking the popu-lation and household travel survey data into account. We generated a commuterpattern based on a gravity model. The gravity model is a classical trip distribu-tion model widely used for trip distribution in an urban context. Other approachesto model transportation networks, namely the queuing model[43], growth factormodel[44], and activity based model using human mobility patterns [45]. These al-ternative approaches are not considered based on (a) methods are data extensiveand (b) some of the techniques required the observed data, which is very difficult togather during the lockdown traffic patterns are completely different when comparedto original traffic mobility. We calculated the trip for road section based on the num-ber of trips attracted to or leaving from specific zones. These trips are distributed atil et al.
Page 6 of 19 by the linking of origin and destination, thus forming an Origin-Destination matrix.The allocation of these trips is done by considering the shortest possible route. Weused the Djikstra algorithm [46] to find the shortest commuter distance. (Equation2) T ij = P i × exp ( − aC ij ) P j (cid:80) ( i,j ) ∈ ( V S × V S ) P j exp ( − aC ij ) (2)Where: • T ij = the number of trips produced in the zone i and attracted to zone j • V S = the set of road intersections in the region S • P i = the population of the i th road intersection • C ij = the minimum time required to go from i th road intersection to j th roadintersection. • a = adjustable parameter to be fixed after model calibration Network Analysis
To understand the network structure’s intricate pattern and relationship, we carriedout the network analysis using a network’s centrality measures . Centrality providesa vital and widely used measure to analyze the network as it helps determine themost critical nodes in the network [38]. Betweenness centrality is an importantcriterion for analyzing centrality, especially in road networks. Road networks includecommuters’ flow along its edges and assuming that people tend to optimize theircommute path by taking the shortest route. We calculated betweenness centrality foreach junction in the network and ranked according to this centrality value (Equation3). The ranks demonstrate the junction’s vulnerability in the network and demarcatethe tendency for high connection with other junctions and can be considered as ameasure for the potential for the junction to develop into congestion points. Weassigned the trip count calculated from the gravity model to each road section(links) and ranked them based on the possible transition. This provides the sectionwith the highest vulnerability in terms of increased traffic flow. Cb ( v ) = (cid:88) u ∈ v (cid:88) w ∈ v/u σ uw ( v ) σ uw (3)Where: • σ uw = the number of shortest paths between u and w • σ uw ( v ) = the number of shortest paths between u and w that passes v Scaling of disease spread
We use the derived transportation network to estimate the spreading of disease inselected regions with comparable population within the cities. The spread of diseaseis dependent on population density. The scaling of disease spread to a city level helpsto understand the behavior of spread in the urban environment. Population densityis used to estimate disease scaling, the relation between them is not always linear.Moreover, this estimate holds true when the extrapolation is done over a small atil et al.
Page 7 of 19 region as the exposure is dependent on the social interaction of the people. Hence,these estimations based on a linear relationship between population density anddisease scaling work effectively when there is uniformity in the community.On a city scale, though, the extent of such predictions is extremely limited due tothe vast diversity in living conditions and connectivity contrast in different regions.Here we have assumed that people’s interaction in a region is more if the connec-tivity inside is competently developed. Based on the above-mentioned criteria, wecalculated the scaling factor to remove a few limitations on the population densitybased extrapolation. The scaling factor for a region S with respect to another region S , κ ( S, S ) is defined in (Equation 4). κ ( S, S ) = N S log N S N S log N S × A ( S ) A ( S ) × F ( S ) F ( S ) (4) • N S = Population of region S • A ( S ) = Area of region S • F ( S ) = Interaction CoefficientHere the F (S) is the independent interaction coefficient of the region and it iscalculated using (Equation 5). F ( S ) = (cid:88) ( i,j ) ∈ ( V S × V S ) exp ( − C ij ) P i P j N S (5)Where: • V S = the set of road intersections in the region S • P i = the population of the i th road intersection • C ij = the minimum time required to go from i th road intersection to j th roadintersection in hours.The route that gives the minimum time, C ij is calculated based on the assumedtravel speed for disparate categories of roads. The complete calculation can bedone using the transport network mentioned in the previous subsection. The valueof F ( S ) is always less than 1 and the square of this value gives the interactioncoefficient for the region S . The exact details for this construction are given in thesupplementary section.The scaling factor we have defined in the Equation 4 is a relative quantity betweenregion S and S o . To provide a single value that can be used to directly quantifymultiple regions and to allow direct comparison between them, we use a base regionfor all calculations. The base region is the identity region I , which is not physicallypresent but an imaginary construct such that N I logN I A ( I ) F ( I ) = 1. Using this identityregion as the base, for any two regions S and S (Equation 6) κ ( S , S ) = κ ( S , I ) κ ( S , I ) (6)For notation purpose, we define κ ( S ) = κ ( S, I ) = N S logN S A ( S ) F ( S ) It is to be noted that the interaction factor is inversely proportional to the scalingfactor. This is because the interaction factor does not consider the area of the region, atil et al.
Page 8 of 19 which is separately considered in the calculation. The construction of the scalingfactor is explained in a supplementary section.
SEIR PLUS model
SEIR PLUS epidemic spread model is applied to scaled-up data to predict thetrajectory of spread. The SEIR model is a standard compartment based model.We used the dynamic form of the model in this study, which is used on stochasticdynamic networks [47]. The equations governing the state of the nodes is explainedin (Equation 7).
P r ( X i = S → E ) = (cid:20) p βIN + (1 − p ) βσ j ∈ C G ( i ) δ X j = I | C G ( i ) | (cid:21) δ X i = S (7) P r ( X i = E → I ) = σδ X i = E P r ( X i = I → R ) = γδ X i = I P r ( X i = I → F ) = µ I δ X i = I P r ( X i = R → S ) = ηδ X i = R For testing purposes and quarantining, the above equations can be modified byadding some more compartments to account for quarantining and testing. The de-tails are discussed in a supplementary section.
The clinical parameters
Parameters such as the rate of transmission, rate of progression, recovery rate,mortality rate depend on the cause of the epidemic. We obtained these parametersfrom the clinical data [48][49]. At the same time, there is also a dependency on therecovery rate when a positive person is detected early on or late.We assumed that these parameters are independent of other factors related to so-cial interaction and lockdown effects. A range was determined using available clinicaldata for such parameters, and fixed values from this range were used throughout.
Setting up the Scenarios
The interventions brought by the Government brings changes in the interactionof people compared to daily life. At the same time, a person detected positivewill reduce the interaction with the rest of the population. To model the differentscenarios, we use Erd˝os-R´eyni graphs with different probabilities for edge creation.These probabilities are seen in the form α/N S for a region S . atil et al. Page 9 of 19
Tuning of parameters
The tunable parameters are the testing rates at different periods. Also, the SEIRmodel requires the number of initially infected people.
Calibration of epidemic spread model
We now detail the steps followed during the calibration cycle: • Pick a single sub-region, say S , and run the SEIR plus model with somearbitrary plausible values for the initial infected parameter, graph α values,and testing rates. • Using the fitting between the observed data for infection and the resuts ofthe SEIR model to fine-tune the values to be used for testing rates and initialinfected rates. • At the same time, change the α parameters but keep them same across allregions. • Check the output for all 10000 population subregions. Do further tuning of α values for the different garphs and also fine tune the testing parametersand initial infected for each region. It must be kept in mind that the initailinfected are set only for 5000 population subregions and scaled values are usedfor 10000 population subregions. • Find a optimal way such that all plots fit with the observed values for all 5000and 10000 population subregions
Results
Our transportation model has two indicators: Betweenness Centrality rank (BCrank) of a road junction (Figure 4(a)) and probable trip count of each road sec-tion(Figure 4(b)). These indicators help to identify densely connected pockets inthe city. Through plotting these results, We have demarcated the possible trafficcongestion pockets in the city. These results show the city pockets vulnerable tospread in post-lockdown scenarios. Our analysis shows that Ahmedabad’s centralregion has high BC rank, demonstrating the priority intersection that can be vul-nerable to disruption due to heavy traffic. The road segments with the high tripcount are located in the city’s central and eastern parts, where population density ishigh. Also, it was seen that the first cases of COVID -19 were observed in this partof the city, making the transportation model useful while considering drive throughtesting.We simulated targeted disruption in the road network to analyze the system’sresponse, which resembles the often seen situations in SARS-CoV-2 spread. Due tomany cases in a particular region, the region might get quarantined or declared acontainment zone. The containment zones make up the proper condition in networkscience that is termed as targeted disruption. The city network is witnessing theinterruption in the traffic flow with the declaration of these containment zones as notravel zones. To analyze the disruption, we removed one of the city’s containmentzones. The possible rerouting shows that this triggers the new potential vulnerableregion to traffic congestion and spread through our re-calibrated indicators (Figure5).The prediction of disease spread is difficult in the diverse living conditions andconnectivity. In that case, we hypothesize that the scaling factor derived from the atil et al.
Page 10 of 19 transportation network model provides a better alternative to population density.It considers the population density and the interaction between the community byroad intersections. The travel time plays a crucial role in determining the scalingfactor. To understand the importance of travel time, we have considered two re-gions with the same populations (Figure 6(a)). The travel time changes with theamount of intersections in the region.That is lesser number of intersections in a aregion would translate to longer transit times, on an average, in an urban setting.This eventually leads to a decrease in the interaction coefficient and an increasein the scaling factor. Using this concept, the population density is calculated frompopulation data (Figure 6(b)) and the scaling factor through interaction coefficient(Figure6(c)) is calculated. Subsequently, we check the hypothesis by determiningthe Kendall-Tau Coefficient generated between the cumulative ward wise infectedcases and the scaling factor and population density, respectively (Figure6(d)). Thisanalysis validates our hypothesis and shows that the scaling factor provides a bettercorrelation compared to the population density (Figure 7(a)) and 7(b)).Once the hypothesis is tested, the calibrated clinical parameters are used to vali-date the prediction of infected population for the regions. The epidemic SEIR plusmodel implemented on sub-regions with disparate ranges of population such as 5000,10000 and 20000 is used to validate the model parameter values (Figure 8(a), (b)and (c)). This approach allows us to account for the variation that comes up withdifferent issues of testing and variation in actual testings when only average testingrates are known. To check the appropriateness of the model the time observations ofduration considered in the testing are the ones, which are not considered during thecalibration by plotting calibration and testing plot simultaneously. For the region1 with 20000 population, the SEIR plus model predicted infected population showsthe good agreement with the observed data. Region-1 shows the R , Relative RootMean Square Error (RRMSE) and Relative Mean Absolute Error (RMAE) valueas 0.9602, 0.688 and 0.558 respectively (Figure 8(d)). The same approach we haveimplemented in region 2, region 3 and region 4 respectively (Figure 9). We evaluatethe prediction performance for the above mentioned region and it is shown in (Table1). The value of R is smaller in the region 4 as the data for SARS-CoV-2 infectedcases in the region was less compared to other regions.The SARS-CoV-2 spread has led governments to think of different interventionsto reduce the spread by implementing various lockdown policies. These policies canchange the trajectory of disease spread. To account this into action, we have alsosimulated the disparate policies in our model by selecting social distancing andrelaxation combinations.The first policy considered is that if the government implements the lockdownrelaxation by last week of May 2020, Unlock with the strict social distancing tillmid-June 2020 and then staged back to a normal state in 50 days. The resultshows that we can expect a sudden spike of cases in the initial days after lockdownrelaxation. However, it gradually decreases in the upcoming months, but it showsthe second wave of cases forming from September 2020 (Figure 10(a)).The second policy we consider is the lockdown reduced by May 2020 end, Unlockwith the strict social distancing followed for 15 days and then staged back to normalstate by mid-July 2020 in a staggered manner. The model result demonstrates atil et al. Page 11 of 19 increased infected cases in the initial days after lockdown relaxation and shows thefluctuation in the infected cases in the September and October 2020 (Figure 10(b)).Lastly, the third policy simulated is that the lockdown reduced by May end,Unlock with the strict social distancing followed for one month and then stagedback to a normal state. The result demarcates that there is a rise in cases in theinitial few days, but after that, from the month of July-2020, it can drop down verylow (Figure 10(c)).
Discussion
The prediction of disease spread at the city scale is often complex due to diverseregional factors and data limitations. The road networks are the prime sourcesof intracity movements. This movement pattern can lead us towards the possiblespreading of disease as most of the infectious diseases spread through social inter-actions. During these scenarios, prediction of disease spread through network-basedepidemic spread models can be very helpful. This study has presented the uniqueapproach to model the disease spread through transportation networks. The resultof this analysis allows several meaningful inferences, which can make a high impacton the prediction of disease spread. First, this approach can be implemented inany congested city to determine the interaction between the population and leadto model disease spread. Most of the data considered during the modeling are opensource or readily available. Second, framework also provides the flexibility of un-derstanding disparate scenarios such as containment zone restriction. The thirdinference gained from the analysis is that the different lockdown policies are highlyinfluenced by social interaction and can be analyzed through the network-basedepidemic spread modeling. Policymakers can choose the best possible way to con-tain the spread. Although the interaction will vary from city to city based on localconditions, we anticipate that the overall patterns will be similar for comparablepopulation densities and road networks. We further note that the quality, quantityand frequency of epidemiological datasets play an important role in establishingthe correlations that we have observed in this study. While the proposed frameworkcan be generalized to other cities, future efforts in this direction can greatly benefitfrom real-time mobility data obtained from cellphone activity or GPS data, andhigh-resolution clinical and epidemiological data with relatively longer duration ofrecord.
Competing interests
The authors declare that they have no competing interests.
Author’s contributions
RP,UB, RD designed the experiments; RP, UB, RD, HP, VS performed the analysis; RP, RD, UB, and DC wrote themanuscript.
Acknowledgements
This work is supported by Startup Research Grant awarded to UB by Indian Institute of Technology Gandhinagar.We are thankful to Prasanna V Balasybramanium, Assistant Professor, Indian Institute of Technology, Gandhinagar,for his helpful comments and suggestions. . . .
Author details Discipline of Computer Science and Engineering, Indian Institute of Technology, Gandhinagar, India. Discipline ofCivil Engineering, Indian Institute of Technology, Gandhinagar, India. Discipline of Mechanical Engineering, IndianInstitute of Technology, Gandhinagar, India. King George Medical University, Lucknow, India. Discipline ofPhysics, Indian Institute of Technology, Gandhinagar, India. atil et al.
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India Gujarat Ahmedabad
Figure 1
Study area of Ahmedabad Municipal Corporation (AMC), located in the central regionof Gujarat in western India. Ahmedabad is selected as area of study given its distinction asfinancial hub of Gujarat, disparate socioeconomic distribution and high population densityatil et al.
Page 14 of 19 (Road Network) Road network Graph Nodes and Links P r e - p r oce ss i n g Population PolygonNodesMinimum BoundingGeometry Thiessen polygon (Voronoi polygons Clip Node Polygon Join JoinSummary StatisticsTabulate IntersectionRaster to polygonPopulation Distribution Node Polygon with population assignedNodes with population assignedBuffer1 km P o p u l a t i o n a ss i g n m e n t T r a ff i c d e m a n d F o r ec a s t a n d N e t w o r k A n a l y s i s Trip –end Prediction/Trip Generation Trip Distribution Trip AssignmentCentrality measures of network Betweennesscentrality of nodes Critical junctions of network Critical edges based on the trip flow S ce n a r i o G e n e r a t i o n A n a l y s i s E p i d e m i c m o d e li n g Road network Targeted disruption Scenario based road network ModelRemoval of highly vulnerable regionRedistribution of weights and ranksCollection of Patient Data Creation of sub region based on patient count Tuning alpha of different alphas to fit smallest sub region Tuning of tunable parameters for all the sub regionsFine tuning Prediction check on complete region Validation of prediction Testing of prediction
Figure 2
Overview of the modeling framework. The proposed methodology consist of (a)Pre-processing, (b) Population assignment, (c) Traffic demand forecast and network analysis, (d)Scenario generation analysis (Targeted disruption) and (e) Epidemic spread modelingatil et al.
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Figure 3 (a) Modeled population data extracted at 30 arc-second , (b) Land use distributiondescribing diverse arrangement of land use in the city ,(c) Bound polygon to consider incomingand outgoing traffic and (d) Assignment of number of population served by junction in a uniqueVoronoi polygons.(red colour is resemblance of high population, where as green colour is for lowpopulation (a) (b)
Figure 4
Maps of Ahmedabad city depicting (a) Road junction distribution according to BC Rank(Red colour nodes depicting high BC rank) and (b) Road network link distribution according totrip count (Red colour road sections depicting high trip count)atil et al.
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Figure 5 (a) The road network without disruption (normal condition), (b) Zoomed in map ofroad network without disruption, (c) Targeted disruption of road network to generate thelockdown scenario by removing containment zone and (SARS-CoV-2 spread situation) (d)Zoomed in map of targeted disruption (a) (b)(c) (d)
Figure 6 (a) Region of interest in the study area for epidemic spread model with samepopulation,(b) Population distribution in the city, (c) Interaction Coefficient distribution in thecity and (d) SARS-CoV-2 Patient Distributionatil et al.
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Date Date (a) (b)
Figure 7 (a) Kendall Tau Correlation and (b) Kendall Tau p- value
Date P opu l a t i on P e r c en t age Date P opu l a t i on P e r c en t age Date P opu l a t i on P e r c en t age Date P opu l a t i on P e r c en t age (a) (b)(d)(c) Figure 8
Region 1 time series data set: (a) Training Data set (1-5000 Population cumulativecases, (b) Training Data set (1-10000 Population cumulative cases), (c) Validation Data set(1-20000 Population cumulative cases) and (d) Prediction Data set (1-20000 Populationcumulative cases)
Date P opu l a t i on P e r c en t age Date P opu l a t i on P e r c en t age Date P opu l a t i on P e r c en t age Figure 9 (a)Testing data sets: Region 2 Data set (1-20000 Population cumulative cases), (b)Region 3 Data set (1-20000 Population cumulative cases) and (c) Region 4 Data set (1-20000Population cumulative cases)atil et al.
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Date P opu l a t i on P e r c en t age Date P opu l a t i on P e r c en t age P opu l a t i on P e r c en t age Date
Figure 10
Time series data of patient count based on different lock down policies (a) Lock downrelaxation by last week of May, Unlock with the strict social distancing till mid June and thenstaged back to normal state in 50 days , (b) Lock down reduced by May end, Unlock with thestrict social distancing followed for 15 days and then staged back to normal state by mid July instaggered manner, (c) Lock down reduced by May end, Unlock with the strict social distancingfollowed for 1 month and then staged back to normal state
Tables
Table 1
Error matrix of prediction depiction the model performance on region of interests R egions (20000 population) R R RMSE R MAE1 0.96 0.68 0.552 0.68 0.73 0.473 0.87 0.41 0.304 0.15 0.71 0.64
Supplementary Materials
Interaction coefficientWe constructed an interaction coefficient based on the gravity model. The interaction between the two intersectionsis determined based on the two parameters: The first one is the fraction of the population in the individualintersections and the second is the time required to travel from one intersection to another. C ij gives theinformation of the time needed by a person while taking the best path possible for travel. C ij is considered zero when i and j intersection are the same. For which the average time required for theinteraction between two persons is believed to be very small. This holds when C ij is measured in terms of hours ordays. This assumption breaks when the measurement is in smaller units as the intra-intersection interaction cannotbe approximated to .Considering the constraint mentioned above, the calculation of C ij is done in terms of hours. The selection of largerunits such as day or month is not considered in the analysis because for the intersection in proximity distance, thetravel time will become negligible, leading to a single intersection. In the city environment, a person can reach anypart of the city and nearby places in the time interval of hours. The unit of time for C ij , in a sense, it defines theresolution at which the system is being observed. If we consider the single interaction in the region S , it is trivial tosee that F ( S ) = 1 . In the case of two intersections, the value of F ( S ) will decrease as C ij (cid:54) = 0 for all terms. Themore the skewed the distribution of population in the region, the smaller is the independent interaction coefficient. F ( S ) only considers the independent interaction between two intersections. But a commuting person may have togo from one intersection to another always through some other intersection. For example, consider that there are intersections in a region S .( Equation 8) F ( S ) = α + α + α + 2( c α α + c α α + c α α ) (8) where α i is the fraction of population for i th intersection and c ij = exp ( − C ij ) .considering (Equation 8) the interaction coefficient is F ( S ) = α + α + α + 4( c α α + c α α + c α α )+ 4( c α α + c α α α + c α α )+ 4( c α α + c α α + c α α α )+ 4( c α α α + c α α + c α α )+ 8( c c α α α + c c α α α + c c α α α )= α + α + α + 4( c α α + c α α + c α α )+ 4( α + α + α )( c α α + c α α + c α α )+ 8 c α α α ( α + c α + c α ) (9) atil et al. Page 19 of 19