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

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