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In this paper, we investigate a stochastic delayed epidemic model with double epidemic hypothesis and vaccination incorporating Lévy noise. First, we show that this model has a unique global positive solution. Furthermore, we give sufficient conditions for extinction and persistence in the mean of the two epidemics and we prove that the two diseases can coexist under some conditions. Finally, we present some examples to illustrate the analytical results by numerical simulations. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

In this paper, we study a stochastic epidemic model with double epidemics which includes white noise and telegraph noise modeled by Markovian switching. Sufficient conditions for the extinction and persistence of the diseases are established. In the end, some numerical simulations are presented to demonstrate our analytical results. [ABSTRACT FROM AUTHOR]