  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 the T cells and
the 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 characteristic 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.
