具有生命动力学的 SIR 模型相平面轨迹的均匀渐近法

IF 1.9 4区数学 Q1 MATHEMATICS, APPLIED SIAM Journal on Applied Mathematics Pub Date : 2024-07-22 DOI:10.1137/23m1576050

Todd L. Parsons, David J. D. Earn

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引用次数: 0

摘要

SIAM 应用数学杂志》，第 84 卷第 4 期，第 1580-1608 页，2024 年 8 月。摘要。我们推导了标准易感-感染-清除（SIR）流行病模型相平面轨迹的精确闭式解析近似值，包括宿主的出生和死亡，给出了瞬态动力学的完整描述。我们对 SIR 常微分方程的近似也使我们能够为相关的 Poincaré 地图以及每个流行波中的最小和最大易感宿主密度和传染性宿主密度提供方便、准确的分析近似。我们的分析涉及兰伯特[math]函数分支切点的匹配渐近展开。

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Uniform Asymptotic Approximations for the Phase Plane Trajectories of the SIR Model with Vital Dynamics

SIAM Journal on Applied Mathematics, Volume 84, Issue 4, Page 1580-1608, August 2024.
Abstract. We derive accurate, closed-form analytical approximations for the phase-plane trajectories of the standard susceptible-infectious-removed (SIR) epidemic model, including host births and deaths, giving a complete description of the transient dynamics. Our approximations for the SIR ordinary differential equations also allow us to provide convenient, accurate analytical approximations for the associated Poincaré map, and the minimum and maximum susceptible and infectious host densities in each epidemic wave. Our analysis involves matching asymptotic expansions across branch cuts of the Lambert [math] function.

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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.