Stochastic Mathematical Modelling Study for Understanding the Extinction, Persistence and Control of SARS-CoV-2 Virus at the Within-host Level

TL;DR

This paper develops a stochastic model for SARS-CoV-2 within-host dynamics, analyzing its stability, extinction conditions, and the impact of environmental noise, with numerical simulations and control strategies.

Contribution

It introduces a stochastic within-host model for SARS-CoV-2, proving stability, extinction conditions, and incorporating control measures, which advances understanding of virus dynamics under uncertainty.

Findings

Environmental noise can lead to disease extinction.

The model's solutions are positive and bounded.

Control measures effectively reduce viral load.

Abstract

Stochastic differential equations characterized by uncertainty are effective in modelling virus dynamics and provide an alternative to traditional deterministic models. Epidemic models are inevitably subjected to the randomness within the system or the environmental noise. In this paper, we analyze the stochastic within host compartment model for SARS-CoV-2 virus and explore its dynamics. We first examine the existence and positivity of the solution of the model using Ito's formula and the establish the stochastic boundedness and permanence of the model. Exponential stability of the infection free equilibrium state is established. Numerical simulations are conducted to complement the theoretical results. Environmental noise is found to play a crucial role in the dynamics of the disease and can even lead to the extinction of the disease. The model is also extended to a stochastic optimal control problem and the effectiveness of control measures, such as antiviral drugs and immunomodulators is investigated.