Abstract
Environmental factors, such as humidity, precipitation, and temperature, have significant impacts on the spread of the new strain coronavirus COVID-19 to humans. In this paper, we use a stochastic epidemic SIRC model, with cross-immune class and time-delay in transmission terms, for the spread of COVID-19. We analyze the model and prove the existence and uniqueness of positive global solution. We deduce the basic reproduction number {mathcal{R}}_{0}^{s} for the stochastic model which is smaller than {mathcal{R}}_{0} of the corresponding deterministic model. Sufficient conditions that guarantee the existence of a unique ergodic stationary distribution, using the stochastic Lyapunov function, and conditions for the extinction of the disease are obtained. Our findings show that white noise plays an important part in controlling the spread of the disease; When the white noise is relatively large, the infectious diseases will become extinct; Re-infection and periodic outbreaks can occur due to the existence of feedback time-delay (or memory) in the transmission terms.
Highlights
The ongoing pandemic coronavirus disease (COVID-19) has become a worldwide emergency
This paper is presented as follows: We provide a stochastic SIRC model with time-delay in Sect
6 Conclusion In this work, we provided a stochastic SIRC epidemic model with time-delay for the new strain coronavirus COVID-19
Summary
The ongoing pandemic coronavirus disease (COVID-19) has become a worldwide emergency. Stochastic perturbation factors, such as precipitation, absolute humidity, and temperature, have a significant impact on the infection force of all types of virus diseases to humans Taking this into consideration enables us to present randomness into deterministic biological models to expose the environmental variability effect, whether it is environmental fluctuations in parameters or random noise in the differential systems [13,14,15,16,17]. In the present paper, we investigate an SIRC epidemic model of crossimmune class for the dynamics of COVID-19 infection among groups. 3, we study the existence and uniqueness of a global positive solution for the stochastic delayed SIRC model.
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