A near analytic solution of a stochastic immune response model considering variability in virus and T-cell dynamics

Biological processes at the cellular level are stochastic in nature, and the immune response system is no different. Therefore, models that attempt to explain this system need to also incorporate noise or fluctuations that can account for the observed variability. In this work, a stochastic model of the immune response system is presented in terms of the dynamics of T cells and virus particles. Making use of the Green's function and the Wilemski-Fixman approximation, this model is then solved to obtain the analytical expression for the joint probability density function of these variables in the early and late stages of infection. This is then also used to calculate the average level of virus particles in the system. Upon comparing the theoretically predicted average virus levels to those of COVID-19 patients, it is hypothesized that the long-lived dynamics that are characteristics of such viral infections are due to the long range correlations in the temporal fluctuations of the virions. This model, therefore, provides an insight into the effects of noise on viral dynamics.