Abstract
In this paper, a stochastic SIRD model of Ebola with double saturated incidence rates and vaccination is considered. Firstly, the existence and uniqueness of a global positive solution are obtained. Secondly, by constructing suitable Lyapunov functions and using Khasminskii’s theory, we show that the stochastic model has a unique stationary distribution. Moreover, the extinction of the disease is also analyzed. Finally, numerical simulations are carried out to portray the analytical results.
Highlights
Ebola virus is a potent virus which causes Ebola hemorrhagic fever in humans and primates
For the spread of Ebola virus, on the basis of models, we divide the total group into four categories: susceptible group S, infected group I, recovered group R, and infected corpse group D
2 Stationary distribution of system (1.3) we construct a suitable Lyapunov function to obtain the conditions of the existence of a unique ergodic stationary distribution to system (1.3)
Summary
Ebola virus is a potent virus which causes Ebola hemorrhagic fever in humans and primates. Considering the above discussion, the deterministic SIRD epidemic model is formulated as follows: Many authors have studied epidemic models with stochastic perturbations As far as we know, the studies on the dynamics of the stochastic SIRD model of Ebola seem to be rare.
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