Stationary distribution and extinction in the stochastic model of human immune system response to COVID-19 virus under regime switching

Abstract

In this paper, in order to study effects of the human immune system response to spread of COVID-19 virus, we establish a stochastic competition model between immune cells and COVID-19 particles by introducing both white and coloured noise. We first prove the existence and uniqueness of the global positive solution of the system under consideration. Furthermore, the stationary distribution and ergodicity of the system are investigated in order to prove weak persistence in mean. We also obtain the conditions for extinction of the disease. The obtained results are related to basic reproduction number of the corresponding deterministic analogue of the system. Finally, we provide numerical simulations with real life data to support theoretical conclusions obtained in the paper.

Keywords

• covid-19 particles
• ergodic stationary distribution
• existence and uniqueness
• extinction
• interaction
• nk cells
• t-cells
• primary 60h10; secondary 92d25