Ma Han, Du Yanyan, Wang Zong, Zhang Qimin
School of Mathematics and Statistics, Ningxia University, Yinchuan, P.R. China.
School of Science, Qingdao University of Technology, Qingdao, P.R. China.
J Comput Biol. 2024 Dec;31(12):1259-1290. doi: 10.1089/cmb.2023.0443. Epub 2024 Sep 27.
Since the stochastic age-structured multigroup susceptible-infected-recovering (SIR) epidemic model is nonlinear, the solution of this model is hard to be explicitly represented. It is necessary to construct effective numerical methods so as to predict the number of infections. In addition, the stochastic age-structured multigroup SIR model has features of positivity and boundedness of the solution. Therefore, in this article, in order to ensure that the numerical and analytical solutions must have the same properties, by modifying the classical Euler-Maruyama (EM) scheme, we generate a positivity and boundedness preserving EM (PBPEM) method on temporal space for stochastic age-structured multigroup SIR model, which is proved to have a strong convergence to the true solution over finite time intervals. Moreover, by combining the standard finite element method and the PBPEM method, we propose a full-discrete scheme to show the numerical solutions, as well as analyze the error estimations. Finally, the full-discrete scheme is applied to a general stochastic two-group SIR model and the Chlamydia epidemic model, which shows the superiority of the numerical method.
由于随机年龄结构多群体易感-感染-恢复（SIR）流行病模型是非线性的，该模型的解难以显式表示。有必要构造有效的数值方法来预测感染人数。此外，随机年龄结构多群体SIR模型具有解的正性和有界性特征。因此，在本文中，为了确保数值解和解析解具有相同的性质，通过修改经典的欧拉-丸山（EM）格式，我们在时间空间上为随机年龄结构多群体SIR模型生成了一种保持正性和有界性的EM（PBPEM）方法，该方法在有限时间区间上被证明对真解具有强收敛性。此外，通过结合标准有限元方法和PBPEM方法，我们提出了一种全离散格式来展示数值解，并分析误差估计。最后，将全离散格式应用于一个一般的随机两组SIR模型和衣原体流行模型，这显示了该数值方法的优越性。
