First order strong convergence and extinction of positivity preserving logarithmic truncated Euler-Maruyama method for the stochastic SIS epidemic model

Abstract

The well-known stochastic SIS model characterized by highly nonlinear in epidemiology has a unique positive solution taking values in a bounded domain with a series of dynamical behaviors. However, the approximation methods to maintain the positivity and long-time behaviors for the stochastic SIS model, while very important, are also lacking. In this paper, based on a logarithmic transformation, we propose a novel explicit numerical method for a stochastic SIS epidemic model whose coefficients violate the global monotonicity condition, which can preserve the positivity of the original stochastic SIS model. And we show the strong convergence of the numerical method and derive that the rate of convergence is of order one. Moreover, the extinction of the exact solution of stochastic SIS model is reproduced. Some numerical experiments are given to illustrate the theoretical results and testify the efficiency of our algorithm.

arXiv comment20 pages, 6figures

References in corpus (8)

• Strong convergence of an explicit numerical method for SDEs with nonglobally Lipschitz continuous coefficients
• Strong and weak divergence in finite time of Euler's method for stochastic differential equations with non-globally Lipschitz continuous coefficients
• Numerical approximations of stochastic differential equations with non-globally Lipschitz continuous coefficients
• A note on tamed Euler approximations
• Euler approximations with varying coefficients: The case of superlinearly growing diffusion coefficients
• Explicit approximations for nonlinear switching diffusion systems in finite and infinite horizons
• Positivity preserving logarithmic Euler-Maruyama type scheme for stochastic differential equations
• Explicit numerical approximation for logistic models with regime switching in finite and infinite horizons