Positivity-Preserving Numerical Method for a Stochastic Multi-Group SIR Epidemic Model

IF 1 4区 数学 Q3 MATHEMATICS, APPLIED Computational Methods in Applied Mathematics Pub Date : 2022-12-07 DOI:10.1515/cmam-2022-0143
Han Ma, Qimin Zhang, X. Xu
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Abstract

Abstract The stochastic multi-group susceptible–infected–recovered (SIR) epidemic model is nonlinear, and so analytical solutions are generally difficult to obtain. Hence, it is often necessary to find numerical solutions, but most existing numerical methods fail to preserve the nonnegativity or positivity of solutions. Therefore, an appropriate numerical method for studying the dynamic behavior of epidemic diseases through SIR models is urgently required. In this paper, based on the Euler–Maruyama scheme and a logarithmic transformation, we propose a novel explicit positivity-preserving numerical scheme for a stochastic multi-group SIR epidemic model whose coefficients violate the global monotonicity condition. This scheme not only results in numerical solutions that preserve the domain of the stochastic multi-group SIR epidemic model, but also achieves the “ order - 1 2 {\mathrm{order}-\frac{1}{2}} ” strong convergence rate. Taking a two-group SIR epidemic model as an example, some numerical simulations are performed to illustrate the performance of the proposed scheme.
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随机多群SIR流行病模型的保正数值方法
随机多群体易感感染恢复(SIR)流行病模型是非线性的,通常难以得到解析解。因此,通常需要寻找数值解,但大多数现有的数值方法都不能保持解的非负性或正性。因此,迫切需要一种合适的通过SIR模型研究传染病动力学行为的数值方法。本文基于Euler-Maruyama格式和对数变换,对系数违反全局单调性条件的随机多群SIR流行病模型,提出了一种新的显式保正数值格式。该方案不仅得到了保持随机多群SIR流行病模型定域的数值解,而且实现了“order - 1 2 {\ mathm {order}-\frac{1}{2}}”的强收敛速率。以两组SIR流行病模型为例,进行了数值模拟,验证了该方法的有效性。
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来源期刊
CiteScore
2.40
自引率
7.70%
发文量
54
期刊介绍: The highly selective international mathematical journal Computational Methods in Applied Mathematics (CMAM) considers original mathematical contributions to computational methods and numerical analysis with applications mainly related to PDEs. CMAM seeks to be interdisciplinary while retaining the common thread of numerical analysis, it is intended to be readily readable and meant for a wide circle of researchers in applied mathematics. The journal is published by De Gruyter on behalf of the Institute of Mathematics of the National Academy of Science of Belarus.
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