Modeling projects

Project hosted at ISRC
Projects involving ISRC members


  • An India-specific compartmental model for Covid19 –Sanit Gupta, Sahil Shah, Sumit Chaturvedi, Pranav Thakkar, Parvinder Solanki, Soham Dibyachintan, Sandeepan Roy, M. B. Sushma, Adwait Godbole, Noufal Jaseem, Pradumn Kumar, Sucheta Ravikanti, Aritra Das, Giridhara R. Babu, Tarun Bhatnagar, Avijit Maji, Mithun K. Mitra, Sai VinjanampathyAbstract — We present a compartmental meta-population model for the spread of Covid-19 in India. Our model simulates populations at a district or state level using an epidemiological model that is appropriate to Covid-19. Different districts are connected by a transportation matrix developed using available census data. We introduce uncertainties in the testing rates into the model that takes into account the disparate responses of the different states to the epidemic and also factors in the state of the public healthcare system. Our model allows us to generate qualitative projections of Covid-19 spread in India, and further allows us to investigate the effects of different proposed interventions. By building in heterogeneity at geographical and infrastructural levels and in local responses, our model aims to capture some of the complexity of epidemiological modeling appropriate to a diverse country such as India.

    A repository for the code and some results that are available in the manuscript is available here.

  • Has the Indian lockdown averted deaths? — Suvrat Raju
    Abstract — This work revisits the question of whether the Indian lockdown has averted deaths. The analysis concludes that epidemiological models cannot provide accurate estimates of this number since there is insufficient data to determine whether the nationwide lockdown has truly averted fatalities, or merely delayed the progression of the pandemic. In fact the author points out that by creating a humanitarian crisis, impacting healthcare for other diseases, and engendering economic insecurity, which has made it harder for people to maintain long-term physical-distancing norms, the Indian lockdown may have exacerbated the challenges of the pandemic instead of providing any relief.
  • Covid-19: an analysis of an extended SEIR model and a comparison of different intervention strategies — Arghya Das, Abhishek Dhar, Srashti Goyal, Anupam Kundu
    Abstract — Modeling accurately the evolution and intervention strategies for the Covid-19 pandemic is a challenging problem. We present here an analysis of an extended Susceptible-Exposed-Infected-Recovered (SEIR) model that accounts for asymptomatic carriers, and explore the effect of different intervention strategies such as social distancing (SD) and testing-quarantining (TQ). The two intervention strategies (SD and TQ) try to reduce the disease reproductive number R0 to a target value of less than 1, but in distinct ways, which we implement in our model equations. We find that for the same target of R being less than 1, TQ is more efficient in controlling the pandemic than lockdowns that only implement SD. However, for TQ to be effective, it has to be based on contact tracing and the ratio of tests/day to the number of new cases/day has to be scaled with the mean number of contacts of an infectious person, which would be high in densely populated regions with low levels of SD. We point out that, apart from R0, an important quantity is the largest eigenvalue of the linearised dynamics which provides a more complete understanding of the disease progression, both pre- and post- intervention, and explains observed data for many countries. Weak intervention strategies (that reduce R0 but not to a value less than 1) can reduce the peak values of infections and the asymptotic affected population. We provide simple analytic expressions for these in terms of the disease parameters and apply them in the Indian context to obtain heuristic projections for the course of the pandemic. We find that the predictions strongly depend on the assumed fraction of asymptomatic carriers.
  • Epidemic parameters for COVID-19 in several regions of India — Sourendu Gupta
    Abstract — Bayesian analysis of publicly available time series of cases and fatalities in different geographical regions of India during April 2020 is reported. It is found that the initial apparent rapid growth in infections could be partly due to confounding factors such as initial rapid ramp-up of disease surveillance. A brief discussion is given of the fallacies which arise if this possibility is neglected. The growth after April 10 is consistent with a time independent but region dependent exponential. From this, R0 is extracted using both known cases and fatalities. The two estimates are seen to agree in many cases; for these CFR is reported. It is seen that CFR and R0 increase together. Some public health implications of this observation are discussed, including a target doubling interval if medical facilities are to remain adequate.
  • Inferring epidemic parameters for COVID-19 from fatality counts in Mumbai — Sourendu Gupta
    Abstract — Epidemic parameters are estimated through Bayesian inference using the daily fatality counts in Mumbai during the period from March 31 to April 14. A doubling time of 5.5 days is observed. In the SEIR model this gives the basic reproduction rate R0 of 3.4. Using as input the infection fatality rate and the interval between infection and death, the number of infections in Mumbai is inferred. It is found that the ratio of the number of test positives to the total infections is 0.13% (median), implying that tests are currently finding 1 out of 750 cases of infection. After correcting for different testing rates, this result is compatible with a measurement of the ratio made recently via serological testing in the USA. From the estimates of the number of infections we infer that the first COVID-19 cases were seeded in Mumbai between late December 2019 and early February 2020. provided the doubling times remained unchanged since then. We remark on some public health implications if the rate of growth cannot be controlled in about a week.
  • Estimating the number of COVID-19 infections in Indian hot-spots using fatality data — Sourendu Gupta and R. Shankar
    Abstract — In India the COVID-19 infected population has not yet been accurately established. As always in the early stages of any epidemic, the need to test serious cases first has meant that the population with asymptomatic or mild sub-clinical symptoms has not yet been analyzed. Using counts of fatalities, and previously estimated parameters for the progress of the disease, we give statistical estimates of the infected population. The doubling time, is a crucial unknown input parameter which affects these estimates, and may differ strongly from one geographical location to another. We suggest a method for estimating epidemiological parameters for COVID-19 in different locations within a few days, so adding to the information required for gauging the success of public health interventions.

Online Symposium

On May 9, a symposium was organised to focus on the wide range of modelling efforts and data analysis being done by various groups in India, for understanding as well as predicting the spread of CoVid 19 epidemic in India.