The Stability Analysis of the Stochastic Infectious Model under Subclinical Infections and the Influence of the Random Noise on Its Stability

Abstract

The stability of the stochastic infectious models under subclinical infections and the influence of the random noise on the stability are considered in this paper. As we all know, the corona virus (COVID-19) has a great impact on economy and society since December 2019. Many people have still been suffering from COVID-19 infection. The control of COVID-19 infection is an emergent issue in epidemiology. One of characteristics of COVID-19 infection is the existence of subclinical infections. Hence, we analyze the stability of the infectious disease under subclinical infections in this paper. In the realistic spread of the infectious disease, environmental change and individual difference cause some kinds of random fluctuations in the model parameters. So, we introduce the random fluctuation into consideration in the model construction and we propose the stochastic infectious models with subclinical infections. Since the stability analysis of the infectious model is effective in the control of the spread of the infectious disease, we analyze the stability of the stochastic infectious model with subclinical infections. By numerical simulations, we show the efficacy of the stability theorems derived in this paper and consider the influence of the random noise on the stability using the Lyapunov exponent.