PDE-based modelling of Covid-19 infections

Projections for confirmed, recovered, active, and deceased Covid-19 cases in India based on our multi-dimensional PDE model Nature Sci Rep 11, 6741 (2021) are provided. The prevalence estimates from serosurveys have been included in the model. However, the scenario curves below show only the officially tested cases for Covid-19.
Model predictions updated on Apr 27, 2021 . For previous results click here (Apr 01, 2021), (Sep 19, 2020), (Aug 06, 2020), (Jun 18, 2020), (May 28, 2020) and (May 3, 2020).
Assumptions of COVID-19 Wave II Model:
  • 30L vaccinated every day, and the efficacy of the vaccine is 70%
  • Two unreported cases for every reported case
  • Lockdown-like restrictions: local lockdown, city lockdown, strict curfew, etc. "Social distance" parameter in the model is fitted similar to the previous year (2020) lockdown
  • Un-lock: Social distance parameter is restored to post-lockdown values of 2020
Scenario Analysis
  • Current Trend (No lockdown, worst-case scenario)
  • 15-day lockdown-like restrictions from 27th April
  • 21-day lockdown-like restrictions from 27th April
  • 30-day lockdown-like restrictions from 27th April
Choose India/State/UT*
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(Click on the above square buttons to remove/add a plot. Use the time slider to adjust time period.)


Computational Model

  • Data* from 23 March, 2021 is used partially to tune the parameters of the data-driven model. These results are current as of Apr 27, 2021.
  • The severity of the infection is taken into consideration while modeling the infectious death rate function (see the rate functions in the model).
  • What if the lockdown-like restrictions are not followed as in 2020?: All projections will follow the Current Trend scenario.
  • What if the post-lockdown "social distance" parameter values follow the pre-lockdown values of 2021 instead of the post-lockdown values of 2020? The spread will be worse, and another scenario analysis needs to be performed.
  • What if the restrictions, inoculation, recovery, and herd immunity improve/worsen compare to the present situation? One can claim that the mathematical model has failed and proven wrong. In reality, we failed the mathematical model by feeding incorrect parameters.
  • State-wise numbers are computed with the national parameters to compare the actual data of the respective state with the national trend. Hence, states' curves are not projections but indicate how the individual state got affected (better/worse) than the national average.
  • Projections and scenario analysis for the state of Karnataka can be found here.

State Performance Compared to National Trend


  1. COVID19-India API
  2. DataMeet/maps
  3. Special thanks to all well wishers and colleagues for the discussion and feedback on our model.
  4. Deepak wishes to acknowledge DST Inspire and Arcot Ramachandran Young Investigator Awards.
  5. Sashi wishes to acknowledge SERB, DST, DRDO, DAAD and AvH for the grants that supported for the development of ParMooN.