Quantitative Biology

The well-known Linear Chain Trick (LCT) allows modelers to derive mean field ODEs that assume gamma (Erlang) distributed passage times, by transitioning individuals sequentially through a chain of sub-states. The time spent in these states is the sum of k exponentially distributed random variables, and is thus gamma (Erlang) distributed. The Generalized Linear Chain Trick (GLCT) extends this technique to the much broader phase-type family of distributions, which includes exponential, Erlang, hypoexponential, and Coxian distributions. Intuitively, phase-type distributions are the absorption time distributions for continuous time Markov chains (CTMCs). Here we review CTMCs and phase-type distributions, then illustrate how to use the GLCT to efficiently build mean field ODE models from underlying stochastic model assumptions. We generalize the Rosenzweig-MacArthur and SEIR models and show the benefits of using the GLCT to compute numerical solutions. These results highlight some practical benefits, and the intuitive nature, of using the GLCT to derive ODE models from first principles.

Originating in Wuhan, the novel coronavirus, severe acute respiratory syndrome 2 (SARS-CoV-2), has astonished health-care systems across globe due to its rapid and simultaneous spread to the neighboring and distantly located countries. To gain the systems level understanding of the role of global transmission routes in the COVID-19 spread, in this study, we have developed the first, empirical, global, index-case transmission network of SARS-CoV-2 termed as C19-TraNet. We manually curated the travel history of country wise index-cases using government press releases, their official social media handles and online news reports to construct this C19-TraNet that is a spatio-temporal, sparse, growing network comprising of 187 nodes and 199 edges and follows a power-law degree distribution. To model the growing C19-TraNet, a novel stochastic scale free (SSF) algorithm is proposed that accounts for stochastic addition of both nodes as well as edges at each time step. A peculiar connectivity pattern in C19-TraNet is observed, characterized by a fourth degree polynomial growth curve, that significantly diverges from the average random connectivity pattern obtained from an ensemble of its 1,000 SSF realizations. Partitioning the C19-TraNet, using edge betweenness, it is found that most of the large communities are comprised of a heterogeneous mixture of countries belonging to different world regions suggesting that there are no spatial constraints on the spread of disease. This work characterizes the superspreaders that have very quickly transported the virus, through multiple transmission routes, to long range geographical locations alongwith their local neighborhoods.

Now that SARS-CoV-2 (COVID-19) vaccines are developed, it is very important to plan its distribution strategy. In this paper, we formulated a multi-objective linear programming model to optimize vaccine distribution and applied it to the agent-based version of our age-stratified and quarantine-modified SEIR with non-linear incidence rates (ASQ-SEIR-NLIR) compartmental model. Simulations were performed using COVID-19 data from Quezon City and results were analyzed under various scenarios: (1) no vaccination, (2) base vaccination (prioritizing essential workers and vulnerable population), (3) prioritizing mobile workforce, (4) prioritizing elderly, and (5) prioritizing mobile workforce and elderly; in terms of (a) reducing infection rates and (b) reducing mortality incidence. After 10 simulations on distributing 500,000 vaccine courses, results show that prioritizing mobile workforce minimizes further infections by 24.14%, which is better than other scenarios. On the other hand, prioritizing the elderly yields the highest protection (439%) for the Quezon City population compared to other scenarios. This could be due to younger people, when contracted the disease, has higher chances of recovery than the elderly. Thus, this leads to reduction of mortality cases.

The nation-wide lockdown starting 25 March 2020, aimed at suppressing the spread of the COVID-19 disease, was extended until 31 May 2020 in three subsequent orders by the Government of India. The extended lockdown has had significant social and economic consequences and `lockdown fatigue' has likely set in. Phased reopening began from 01 June 2020 onwards. Mumbai, one of the most crowded cities in the world, has witnessed both the largest number of cases and deaths among all the cities in India (41986 positive cases and 1368 deaths as of 02 June 2020). Many tough decisions are going to be made on re-opening in the next few days. In an earlier IISc-TIFR Report, we presented an agent-based city-scale simulator(ABCS) to model the progression and spread of the infection in large metropolises like Mumbai and Bengaluru. As discussed in IISc-TIFR Report 1, ABCS is a useful tool to model interactions of city residents at an individual level and to capture the impact of non-pharmaceutical interventions on the infection spread. In this report we focus on Mumbai. Using our simulator, we consider some plausible scenarios for phased emergence of Mumbai from the lockdown, 01 June 2020 onwards. These include phased and gradual opening of the industry, partial opening of public transportation (modelling of infection spread in suburban trains), impact of containment zones on controlling infections, and the role of compliance with respect to various intervention measures including use of masks, case isolation, home quarantine, etc. The main takeaway of our simulation results is that a phased opening of workplaces, say at a conservative attendance level of 20 to 33\%, is a good way to restart economic activity while ensuring that the city's medical care capacity remains adequate to handle the possible rise in the number of COVID-19 patients in June and July.

As 2021 dawns, the COVID-19 pandemic is still raging strongly as vaccines finally appear and hopes for a return to normalcy start to materialize. There is much to be learned from the pandemic's first year data that will likely remain applicable to future epidemics and possible pandemics. With only minor variants in virus strain, countries across the globe have suffered roughly the same pandemic by first glance, yet few locations exhibit the same patterns of viral spread, growth, and control as the state of Hawai'i. In this paper, we examine the data and compare the COVID-19 spread statistics between the counties of Hawai'i as well as examine several locations with similar properties to Hawai'i.

The study carries out predictive modeling based on publicly available COVID-19 data for the duration 01 April to 20 June 2020 pertaining to India and five of its most infected states: Maharashtra, Tamil Nadu, Delhi, Gujarat, and Rajasthan using susceptible, infected, recovered, and dead (SIRD) model. The basic reproduction number R0 is derived by exponential growth method using RStudio package R0. The differential equations reflecting SIRD model have been solved using Python 3.7.4 on Jupyter Notebook platform. For visualization, Python Matplotlib 3.2.1 package is used. The study offers insights on peak-date, peak number of COVID-19 infections, and end-date pertaining to India and five of its states. The results could be leveraged by political leadership, health authorities, and industry doyens for policy planning and execution.

Background: Without proven effect treatments and vaccines, Social Distancing is the key protection factor against COVID-19. Social distancing alone should have been enough to protect again the virus, yet things have gone very differently, with a big mismatch between theory and practice. What are the reasons? A big problem is that there is no actual social distancing data, and the corresponding people behavior in a pandemic is unknown. We collect the world-first dataset on social distancing during the COVID-19 outbreak, so to see for the first time how people really implement social distancing, identify dangers of the current situation, and find solutions against this and future pandemics. Methods: Using a sensor-based social distancing belt we collected social distance data from people in Italy for over two months during the most critical COVID-19 outbreak. Additionally, we investigated if and how wearing various Personal Protection Equipment, like masks, influences social distancing. Results: Without masks, people adopt a counter-intuitively dangerous strategy, a paradox that could explain the relative lack of effectiveness of social distancing. Using masks radically changes the situation, breaking the paradoxical behavior and leading to a safe social distance behavior. In shortage of masks, DIY (Do It Yourself) masks can also be used: even without filtering protection, they provide social distancing protection. Goggles should be recommended for general use, as they give an extra powerful safety boost. Generic Public Health policies and media campaigns do not work well on social distancing: explicit focus on the behavioral problems of necessary mobility are needed.

As the ravages caused by COVID-19 pandemic are becoming inevitable with every moment, monitoring and understanding of transmission and fatality rate has become even more paramount for containing its spread. The key purpose of this analysis is to report the real-time effective reproduction rate ( R t ) and case fatality rates (CFR) of COVID-19 in South Asia region. Data for this study are extracted from JHU CSSE COVID-19 Data source up to July 31, 2020. R t is estimated using exponential growth and time-dependent methods. R0 package in R-language is employed to estimate R t by fitting the existing epidemic curve. Case fatality rate is estimated by using Naive and Kaplan-Meier methods. Owing to exponential increase in cases of COVID-19, the pandemic will ensue in India, Maldives and in Nepal as R t was estimated greater than 1 for these countries. Although case fatality rates are found lesser as compared to other highly affected regions in the world, strict monitoring of deaths for better health facilities and care of patients is emphasized. More regional level cooperation and efforts are the need of time to minimize the detrimental effects of the virus.

The infectivity profile of an individual with COVID-19 is attributed to the paper Temporal dynamics in viral shedding and transmissibility of COVID-19 by He et al., published in Nature Medicine in April 2020. However, the analysis within this paper contains a mistake such that the published infectivity profile is incorrect and the conclusion that infectiousness begins 2.3 days before symptom onset is no longer supported. In this document we discuss the error and compute the correct infectivity profile. We also establish confidence intervals on this profile, quantify the difference between the published and the corrected profiles, and discuss an issue of normalisation when fitting serial interval data. This infectivity profile plays a central role in policy and decision making, thus it is crucial that this issue is corrected with the utmost urgency to prevent the propagation of this error into further studies and policies. We hope that this preprint will reach all researchers and policy makers who are using the incorrect infectivity profile to inform their work.

Background: One of the most challenging keys to understand COVID-19 evolution is to have a measure on those mild cases which are never tested because their few symptoms are soft and/or fade away soon. The problem is not only that they are difficult to identify and test, but also that it is believed that they may constitute the bulk of the cases and could be crucial in the pandemic equation. Methods: We present a novel algorithm to extract the number of these mild cases by correlating a COVID-line calls to reported cases in given districts. The key assumption is to realize that, being a highly contagious disease, the number of calls by mild cases should be proportional to the number of reported cases. Whereas a background of calls not related to infected people should be proportional to the district population. Results: We find that for Buenos Aires Province, in addition to the background, there are in signal 6.6 +/- 0.4 calls per each reported COVID-19 case. Using this we estimate in Buenos Aires Province 20 +/- 2 COVID-19 symptomatic cases for each one reported. Conclusions: A very simple algorithm that models the COVID-line calls as sum of signal plus background allows to estimate the crucial number of the rate of symptomatic to reported COVID-19 cases in a given district. The result from this method is an early and inexpensive estimate and should be contrasted to other methods such as serology and/or massive testing.