First order strong convergence of positivity preserving logarithmic Euler–Maruyama method for the stochastic SIS epidemic model

Abstract

In this article, we first construct a positivity-preserving numerical method for the stochastic Susceptible–Infected–Susceptible (SIS) epidemic model by combining the logarithmic transformation and Euler–Maruyama (EM) method. Then, we show that the algorithm not only preserves the domain of the original SDE, but also has the first-order rate of the pth-moment convergence over a finite time interval for all p>0. Finally, some numerical experiments are provided to illustrate the theoretical results.