Mathematical Sciences

Title :

Modelling the spread of COVID-19 viral infection at the cellular level

Area of research :

COVID-19 Research, Life Sciences & Biotechnology, Mathematical Sciences

Focus area :

Mathematical modelling for COVID-19

Principal Investigator :

Dr Rati Sharma, Assistant Professor, Indian Institute of Science Education and Research (IISER), Bhopal

Timeline Start Year :


Contact info :


Executive Summary :

The ongoing pandemic due to the spread of the viral infection, COVID-19, calls into focus a renewed look into modelling of viral dynamics. Systems biology-based models have, in the past, been successful in modelling the HIV and T-lymphocyte dynamics. Therefore, it is pertinent to develop models specific to the in-host spread of SARS-CoV-2 by building upon past successful studies. Through this proposal, a mathematical model is developed to explain the dynamics of the virus and the susceptible and infected cells in addition to the effect of any retroviral drug or immunotherapy procedures. One of the unique features of this virus is the long incubation period followed by a long replication period, which totals to around 14-21 days. Here, the heterogeneities in the rates of viral infection will be introduced using a memory kernel, which in turn is related to the noise through the fluctuation dissipation theorem. The model will be compared to RT-PCR data of nasal or throat swabs that reveal the temporal dynamics of viral load per mL of cell. Therefore, the model will not only be used to check for its validity and future applications but also propose new dynamics under inhibitory conditions that arise due to drug action.


Understanding the functioning and dynamics of the immune system becomes important given the role that it plays in fighting off infection and disease. In this study, a stochastic version of the immune response model have been developed and analysed. In this work, the Fokker-Planck equation has been derived, which is then used to compute the joint probability distribution of T cells and virus particles by making use of the Wilemski-Fixman approximation. This approach allows to obtain analytical solutions of the probability distribution functions and the average virus particles in the limit of short and long times, showing how the infection begins and ends. Carried out a comparison with the available SARS-CoV-2 virus data from patients in Germany. At short times, i.e., during the early period of infection, the model predicts that there is a steep rise in the virus levels with time, whereas, at long times, the virus levels drop gradually, in accordance with the model's prediction.

Organizations involved