Dynamics of a stochastic COVID-19 epidemic model with jump-diffusion

Abstract

For a stochastic COVID-19 model with jump-diffusion, we prove the existence and uniqueness of the global positive solution. We also investigate some conditions for the extinction and persistence of the disease. We calculate the threshold of the stochastic epidemic system which determines the extinction or permanence of the disease at different intensities of the stochastic noises. This threshold is denoted by ξ which depends on white and jump noises. The effects of these noises on the dynamics of the model are studied. The numerical experiments show that the random perturbation introduced in the stochastic model suppresses disease outbreak as compared to its deterministic counterpart. In other words, the impact of the noises on the extinction and persistence is high. When the noise is large or small, our numerical findings show that COVID-19 vanishes from the population if $\xi <1$ ξ < 1 ; whereas the epidemic cannot go out of control if $\xi >1$ ξ > 1 . From this, we observe that white noise and jump noise have a significant effect on the spread of COVID-19 infection, i.e., we can conclude that the stochastic model is more realistic than the deterministic one. Finally, to illustrate this phenomenon, we put some numerical simulations.

Analytical insights of the effects of Non-Pharmaceutical Interventions on SRAS-CoV-2 Dynamic with Application to West African Data

“…In COVID-19 modeling, different types of models are used to understand SARS-CoV-2 transmission, such as deterministic models, stochastic models [18][19][20][21][22][23][24][25], agent-based models [26,27], discrete models [28,29], spatial models [30][31][32], network models [33,34], etc. COVID-19 stochastic models are sometimes compartmental models with the introduction of white noise, such as Gaussian noise or Brownian noise, to create randomness in order to find the condition of extinction and persistence on average of the disease and to prove the existence and uniqueness of the global positive solution of the model.…”

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

“…However, natural and massive phenomena such as Covid-19, earthquakes, tsunamis, and volcanoes cannot be modeled by the stochastic differential equation because these phenomena cause to break the continuity of the solution and provoke jumps in the system. Consequently, including a jump process (Lévy process [30,37,38]) in a stochastic system may well model these phenomena. This paper is aimed at studying the effect of environmental fluctuations on the model (1).…”

Modeling the stochastic within-host dynamics SARS-CoV-2 infection with discrete delay

“…( 2021 ); Zhang and Alzahrani ( 2020 ); Tesfay et al. ( 2021 ) and with discrete delay in El-Metwally et al. ( 2021 ); Almutairi et al.…”