Domain preserving and strongly converging explicit scheme for the stochastic SIS epidemic model

TL;DR

This paper introduces a new explicit numerical scheme for stochastic SIS epidemic models, proving its strong convergence and stability, to improve the accuracy and efficiency of numerical solutions for stochastic differential equations in epidemiology.

Contribution

The paper develops a domain-preserving, strongly convergent explicit scheme for stochastic SIS models, which is novel in ensuring stability and convergence for such epidemic models.

Findings

The proposed scheme has strong convergence order 1.

It maintains stability properties of the stochastic SIS model.

Numerical experiments demonstrate improved accuracy over existing methods.

Abstract

In this article, we construct a numerical method for a stochastic version of the Susceptible Infected Susceptible (SIS) epidemic model, expressed by a suitable stochastic differential equation (SDE), by using the semi-discrete method to a suitable transformed process. We prove the strong convergence of the proposed method, with order $1,$ and examine its stability properties. Since SDEs generally lack analytical solutions, numerical techniques are commonly employed. Hence, the research will seek numerical solutions for existing stochastic models by constructing suitable numerical schemes and comparing them with other schemes. The objective is to achieve a qualitative and efficient approach to solving the equations. Additionally, for models that have not yet been proposed for stochastic modeling using SDEs, the research will formulate them appropriately, conduct theoretical analysis of the model properties, and subsequently solve the corresponding SDEs.