On the Stability Analysis for the Stochastic Infectious Model under Subclinical Infections and Vaccination with Waning Immunity

Abstract

This paper is concerned with the mathematical analysis of the stochastic infectious model under subclinical infections and vaccination and waning immunity. In the modern society with the advanced medical technology, we have still various kinds of the infectious disease threat including Coronavirus disease (Covid-19). Hence, the control and the analysis of infection diseases is one of major problems in epidemiology. In the control of the infectious diseases, vaccination plays an important role. In the realistic spread of the infectious disease, environmental change and individual difference cause some kinds of random fluctuations in the infection and the recovery rates. Moreover, noting that one of characteristics of Covid-19 is the existence of subclinical infections, we propose the stochastic infectious model under subclinical infections and vaccination with waning immunity. 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. We derive the stability conditions for the proposed stochastic infectious model to be stable. By numerical simulations, we show the efficacy of the stability theorems derived in this paper and we study the influence of the random noise and vaccination on the stability.