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 $l^1\left(\mathbb{R}\right)$-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.

本文针对随机年龄结构的人口模型，考虑了基于隐式欧拉方法（IM）的完全离散化方案。显示了根据生物学意义以适当的数值边界条件保存的总种群。基本生殖数字的明确公式${\mathrm{[R}}^H$ 是通过将数值过程嵌入到 ${升}^{\mathrm{1个}}（\mathbb{[R}）$无限随机Leslie算子的高值可积随机过程。此外，两者之间的融合和联系${\mathrm{[R}}^H$并分析了数值解的稳定性。对于小步长，讨论了通过数值解保存和检测解析稳定性的问题。最后，一些数值实验（包括针对SARS流行的感染年龄模型）证明了我们分析的有效性和有效性。