THE IMPACT OF STOCHASTIC ENVIRONMENT ON PSYCHOLOGICAL HEALTH DYNAMICS

Abstract

A mathematical model has been proposed to consider two distinct forms of psychological pressure that arise due to the COVID-19 situation and their impact on individuals’ lives, including their mental well-being and happiness. For a more realistic situation, the effect of stochasticity should be taken into account. Hence, our paper mainly investigates the effect of stochastically environmental variability on the transmission dynamics of psychological stress. We obtain two thresholds [Formula: see text] and [Formula: see text]. If [Formula: see text], the psychological stress will persist and there will be a unique stationary distribution; whereas if [Formula: see text], the extinction of psychological stress is obtained. Moreover, we display the mean first passage time from the initial value to the state of disappearance in order to examine the impact of environmental disturbances; meanwhile, we conduct numerical simulations to illustrate the theoretical findings.