The Influence of Lévy Noise and Independent Jumps on the Dynamics of a Stochastic COVID-19 Model with Immune Response and Intracellular Transmission

The coronavirus (COVID-19) expanded rapidly and affected almost the whole world since December 2019. COVID-19 has an unusual ability to spread quickly through airborne viruses and substances. Taking into account the disease’s natural progression, this study considers that viral spread is unpredictable rather than deterministic. The continuous time Markov chain (CTMC) stochastic model technique has been used to anticipate upcoming states using random variables. The suggested study focuses on a model with five distinct compartments. The first class contains Lévy noise-based infection rates (termed as vulnerable people), while the second class refers to the infectious compartment having similar perturbation incidence as the others. We demonstrate the existence and uniqueness of the positive solution of the model. Subsequently, we define a stochastic threshold as a requisite condition for the extinction and durability of the disease’s mean. By assuming that the threshold value R0D is smaller than one, it is demonstrated that the solution trajectories oscillate around the disease-free state (DFS) of the corresponding deterministic model. The solution curves of the SDE model fluctuate in the neighborhood of the endemic state of the base ODE system, when R0P>1 elucidates the definitive persistence theory of the suggested model. Ultimately, numerical simulations are provided to confirm our theoretical findings. Moreover, the results indicate that stochastic environmental disturbances might influence the propagation of infectious diseases. Significantly, increased noise levels could hinder the transmission of epidemics within the community.