The convergence and stability of full discretization scheme for stochastic age-structured population models.

• A fully discretization scheme by the implicit Euler method for stochastic population models. • The preservation of the total population with a "suitable" numerical boundary condition. • The proposed numerical basic reproduction number R h through embedded infinite stochastic Leslie operators. • The preservation and detection of the analytic stability through numerical solutions for small stepsize. In this paper, a fully discretization scheme based on the implicit Euler method (IM) is considered for stochastic age-structured population models. The preservation of the total population with a suitable numerical boundary condition according to the biological meanings are shown. An explicit formula of the numerical basic reproductive number R h is proposed by the technique that the numerical process is embedded into an l 1 (R) -valued integrable stochastic process with infinite stochastic Leslie operators. Furthermore, the convergence and connection between R h and the stability of numerical solution is analyzed. The preservation and detection of the analytic stability through the numerical solutions are discussed for small stepsize. Finally, some numerical experiments including an infection-age model for modified SARS epidemic illustrate the verification and efficiency of our analysis. [ABSTRACT FROM AUTHOR]