Strong convergence of the partially truncated Euler–Maruyama scheme for a stochastic age-structured SIR epidemic model

Abstract

we study in this paper strong convergence of the partially truncated Euler-Maruyama scheme for an age-structured Susceptible-Infected-Removed (SIR) epidemic model with environmental noise. Using the semigroup theory, the existence and uniqueness of global positive solution for the model is first proved. We then define a truncated function and develop a partially truncated EM numerical solutions to the stochastic age-structured SIR epidemic model. We present the pth moment boundedness of the partially truncated EM numerical approximate solutions under appropriate conditions. Furthermore, the strong Lq convergence is established for the condition of 2 ≤ q < p of the partially truncated EM scheme. Finally, numerical simulations and examples are provided to demonstrate theoretical results and to illustrate validity of the partially truncated EM scheme.