SIR Model for Households

IF 1.9 4区数学 Q1 MATHEMATICS, APPLIED

SIAM Journal on Applied Mathematics Pub Date : 2024-07-11 DOI:10.1137/23m1556861

Philipp Dönges, Thomas Götz, Nataliia Kruchinina, Tyll Krüger, Karol Niedzielewski, Viola Priesemann, Moritz Schäfer

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引用次数: 0

Abstract

SIAM Journal on Applied Mathematics, Volume 84, Issue 4, Page 1460-1481, August 2024.
Abstract. Households play an important role in disease dynamics. Many infections happen there due to the close contact, while mitigation measures mainly target the transmission between households. Therefore, one can see households as boosting the transmission depending on household size. To study the effect of household size and size distribution, we differentiated within and between household reproduction rates. There are basically no preventive measures, and thus the close contacts can boost the spread. We explicitly incorporated that typically only a fraction of all household members are infected. Thus, viewing the infection of a household of a given size as a splitting process generating a new small fully infected subhousehold and a remaining still susceptible subhousehold, we derive a compartmental ODE model for the dynamics of the subhouseholds. In this setting, the basic reproduction number as well as prevalence and the peak of an infection wave in a population with given household size distribution can be computed analytically. We compare numerical simulation results of this novel household ODE model with results from an agent-based model using data for realistic household size distributions of different countries. We find good agreement of both models showing the catalytic effect of large households on the overall disease dynamics.

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家庭 SIR 模型

SIAM 应用数学杂志》第 84 卷第 4 期第 1460-1481 页，2024 年 8 月。摘要家庭在疾病动力学中扮演着重要角色。由于密切接触，许多传染病都发生在住户中，而缓解措施主要针对住户之间的传播。因此，我们可以认为家庭的规模会促进疾病的传播。为了研究家庭规模和规模分布的影响，我们区分了家庭内部和家庭之间的繁殖率。基本上没有预防措施，因此密切接触会促进传播。我们明确指出，通常只有一小部分家庭成员会受到感染。因此，我们将给定规模的家庭感染视为一个分裂过程，产生一个新的完全感染的小分户和一个剩余的仍然易感的分户。在这种情况下，可以通过分析计算给定家庭规模分布的人口中的基本繁殖数、流行率和感染波峰值。我们将这种新型家庭 ODE 模型的数值模拟结果与使用不同国家现实家庭规模分布数据的基于代理的模型结果进行了比较。我们发现这两个模型的结果非常吻合，显示了大户对整个疾病动态的催化作用。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

SIAM Journal on Applied Mathematics 数学-应用数学

CiteScore

3.60

自引率

0.00%

发文量

审稿时长

12 months

期刊介绍： SIAM Journal on Applied Mathematics (SIAP) is an interdisciplinary journal containing research articles that treat scientific problems using methods that are of mathematical interest. Appropriate subject areas include the physical, engineering, financial, and life sciences. Examples are problems in fluid mechanics, including reaction-diffusion problems, sedimentation, combustion, and transport theory; solid mechanics; elasticity; electromagnetic theory and optics; materials science; mathematical biology, including population dynamics, biomechanics, and physiology; linear and nonlinear wave propagation, including scattering theory and wave propagation in random media; inverse problems; nonlinear dynamics; and stochastic processes, including queueing theory. Mathematical techniques of interest include asymptotic methods, bifurcation theory, dynamical systems theory, complex network theory, computational methods, and probabilistic and statistical methods.