The Power of Delay on a Stochastic Epidemic Model in a Switching Environment

Abstract

In recent years, the world knew many challenges concerning the propagation of infectious diseases such as avian influenza, Ebola, SARS-CoV-2, etc. These epidemics caused a change in the healthy balance of humanity. Also, the epidemics disrupt the economies and social activities of countries around the world. Mathematical modeling is a vital means to represent and control the propagation of infectious diseases. In this paper, we consider a stochastic epidemic model with a Markov process and delay, which generalizes many models existing in the literature. In addition, we show the stochastic threshold for the extinction of the disease. Furthermore, numerical examples are discussed to confirm the theoretical result.

The Impact of Random Noise on the Dynamics of COVID-19 Epidemic Model

“…Then, random fluctuations affect the distribution of infectious diseases since this type of epidemic spreads randomly. Therefore, some authors have expressed the random effect in their deterministic models by employing the direct perturbation of parameter approach [32][33][34][35]. For example, El Koufi et al in [26] have assumed that the stochastic perturbations are of white noise type and affect the transmission rate of disease.…”

Nonlinear Stochastic SIS Epidemic Model Incorporating Lévy Process

“…Among the models proposed, the classic SIR epidemic model of Kermack and McKendrick is widely used [1] which divides the population into three classes, namely, susceptible (S), infected (I), and recovered (R). As a result, other works have generalized the Kermack-McKendrick (see, for example, [2][3][4][5][6][7][8]) model. On the other hand, for some diseases such as bacterial diseases and some sexually transmitted diseases, the SIR model is not suitable because the individuals infected with these diseases start to be susceptible, at a certain stage get the disease, and after a short infectious period become susceptible again [9,10].…”