PDE-based modelling of Covid-19 infections

The developed model is a paradigm shift in mathematical modeling of infectious diseases.
We provide prediction of all India and state-wise confirmed, recovered, active and deceased Covid-19 cases based on our multi-dimensional PDE model, Nature Sci Rep 11, 6741 (2021). The prevalance estimates from sero-surveys have been included in the model. However, the scenario curves below show only cases that will officially be tested for Covid-19.
Model predictions updated on Apr 01, 2021 (Current Trend added on 6 Apr). For previous results click here (Sep 19, 2020), (Aug 06, 2020), (Jun 18, 2020), (May 28, 2020) and (May 3, 2020).
COVID-19 Wave II projections with assumptions:
  • Spread is similar to 23 Mar - 1 Oct '20,
  • 30L vaccinated every day, and the efficacy of the vaccine is 70%
  • 20X prevalence factor based on serosurveys
Scenario Analysis
  • Current Trend: 10x Sero Factor
  • Wave II: Assumptions as above
  • Better: 30x Sero Factor
  • Worse: 2x Sero Factor
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, 2020 is used partially to tune the parameters of the data-driven model. These results are current as of Apr 01, 2021.
  • Quarantine of Active Cases so as to prevent new infections is the key to contain the pandemic. An adaptive quarantine function in our model ensures that infected population is quarantined based on their infection level (showing symptoms) and based on latest published literature on how the infection spreads from infected population.
  • The severity of the infection is taken into consideration while modeling the infectious death rate function (see the rate functions in the model).

Summary of Wave II Scenario

  • IND: 1.36cr by 1 May'21 and 1.53cr by 1 Sep'21 will get infected in India, whereas the peak will be around the mid of April with a maximum active case of 7.3L.
  • KA: 10.7L by 1 May'21 and 11.2L by Sep'21 will get infected in Karnataka, whereas the peak will be around the mid of April with a maximum active case of 36K.
  • TN: 9.5L by 1 May'21 and 10.1L by Sep'21 will get infected in Tamilnadu, whereas the peak will be around the mid of April with a maximum active case of 27K.


  • Current Trend projection, which is computed with 10X factor, seems to be matching with the actual data. It indicates that a better social distancing norms need to be implemented/followed to follow Wave II or Better scenarios.

State Performance Compared to National Trend


  1. COVID19-India API
  2. DataMeet/maps
  3. Members of eXComp group, CDS, IISc Bangalore
  4. Special thanks to all well wishers and colleagues for the discussion and feedback on our model.
  5. We thank the Indian Academy of Science Summer Fellowship Program for the support to Chris.
  6. Deepak wishes to acknowledge DST Inspire and Arcot Ramachandran Young Investigator Awards.
  7. Sashi wishes to acknowledge SERB, DST, DRDO, DAAD and AvH for the grants that supported for the development of ParMooN.