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. The prevalance estimates from sero-surveys have been included in the model. However, the scenario curves below show only cases that will officialy be tested for Covid-19.
Model predictions updated on Sep 19, 2020 . For previous results click here (Aug 06, 2020), (Jun 18, 2020), (May 28, 2020) and (May 3, 2020).
Scenario Analysis
  • S1: Assume that 10 times (10x) the confirmed positive Covid-19 cases prevalent in the population.
  • S2: S1 with a vaccine introduced on 1 January 2021.
  • S3: S1 with a vaccine introduced on 1 April 2021.
  • S4: Assume that 20 times (20x) the confirmed positive Covid-19 cases prevalent in the population.
  • S5: S4 with a vaccine introduced on 1 January 2021.
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* between 23 Mar and 31 Aug, 2020 is used partially to tune the parameters of the data-driven model. These results are current as of Sep 19, 2020.
  • 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).


  • A prevalence factor of 10x and 20x mean that only 10% and 5% of the total number of infected cases in the population are reported.
  • In both 10x and 20x scenarios, the total number of cases (reported + unreported) is close to 50% of the total population. However, in the 10x scenario, more cases are reported than in 20x.
  • For 10x preavalence factor, the availability of vaccine from 1 Jan and 1 Apr, reduce the total reported cases by 42% and 12% respectively by the end of 2021.
  • To end the pandemic by Dec 2021 under the present conditions, the vaccination should start atleast by 1 Apr 2021.
  • Until the development of vaccines, social distancing and other practices to reduce interaction among people (such as avoiding mass gathering etc.) are the key tools to contain the spread of COVID-19. As such, public awareness of these practices through several modes (advertisements through TV, radios, new papers, social media, etc.) is crucial.
  • The forecast range of all predicted scenarios (some shown here, others not shown) can be viewed by enabling the uncertainty region in the time series plots. The region may be interpreted as the "Confidence Interval" for the forecast numbers.

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.