The balanced implicit method of preserving positivity for the stochastic SIQS epidemic model

Abstract The main purpose of this paper is to develop a numerical method preserving positivity for a stochastic SIQS epidemic model which is an effective tactics for forecasting and controlling infectious diseases. By the explicit Euler–Maruyama (EM) scheme, we can obtain a numerical approximate solution of the stochastic SIQS epidemic model. We will explore the convergence property of the EM approximate solution to the true solution. However, the explicit EM scheme has it own defection because of the influence of environmental fluctuation, it may not preserve positivity of numerical solution. Therefore, we will construct a balanced implicit numerical method which motivated by Schurz in Schurz (1996). It is confirmed that the Balanced Implicit Method (BIM) can preserve positivity. We prove that the BIM approximate solution will converge to the true solution. By numerical simulations to verify the positivity of solution and the efficiency of our proposed numerical method.

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