Random dynamics of an SIV epidemic model

Abstract

Vaccines train the immune system to create antibodies when it has been exposed to a disease. They protect against many different diseases, including Hepatitis B, Influenza, Polio, etc. This paper considers the vaccination process by including individuals who have started the vaccination process in the transmission model. By the non-parametric perturbation technique, we shall formulate the stochastic SIV model. The examination of the deterministic model relies on the global Lipschitz condition, a crucial factor in guaranteeing the uniqueness and stability of solutions to the model’s differential equation. In contrast, our scrutiny of the stochastic model is rooted in the local Lipschitz condition, which proves to be more applicable and realistic in the context of real-world scenarios. Analysis of the stochastic models may be superior to the analysis of the deterministic models. In many cases, surprisingly, analysis of the stochastic models may provide results that are close to the results obtained from the analysis of the deterministic models. However, it comes with a cost, namely, we might not predict the pattern or the random probability distribution of the stochastic system, moreover, the necessary conditions for the extinction of the disease are weaker compared to the deterministic model. The impact of the continuous vaccination strategy on disease spread is demonstrated. Our results reveal that the vaccination process is very helpful and useful in eradicating the disease. Using MATHEMATICA software and MATLAB software, stability regions of the disease-free equilibrium are presented.