Infection-age structured epidemic models with behavior change or treatment
Infection-age structured epidemic models with behavior change or treatment
复制标题
DOI：
10.1080/17513750601040383
复制
发表时间：
2007-01-01
影响因子：
2.8
通讯作者：
Li, Jia
中科院分区：
文献类型：
--
作者：
Hyman, James M.;Li, Jia
我们制定感染年龄结构易感感染去除（SIR）模型与行为改变或治疗感染。个人在感染后会改变自己的行为或接受治疗。以感染年龄为连续变量，将感染者分为不同感染阶段的离散组，分别建立了考虑行为改变或治疗的偏微分方程模型和常微分方程模型。通过对无感染平衡的线性稳定性分析，我们推导出了繁殖数的显式公式，以及两种模型的唯一地方性平衡存在时的显式公式。这些公式为分析行为改变或感染治疗对传染病传播动力学的影响提供了数学理论框架。研究了几种特殊情况，并在此基础上给出了繁殖数对模型参数的敏感性分析。
We formulate infection-age structured susceptible-infective-removed (SIR) models with behavior change or treatment of infections. Individuals change their behavior or have treatment after they are infected. Using infection age as a continuous variable, and dividing infectives into discrete groups with different infection stages, respectively, we formulate a partial differential equation model and an ordinary differential equation model with behavior change or treatment. We derive explicit formulas for the reproductive number by linear stability analysis of the infection-free equilibrium, and explicit formulas for the unique endemic equilibrium, when it exists, for both models. These formulas provide mathematical theoretical frameworks for analysis of impact of behavior change or treatment of infection to the transmission dynamics of infectious diseases. We study several special cases and provide sensitivity analysis for the reproductive numbers with respect to model parameters based on those formulas.