Application of an age-structured deterministic endemic model for disease control in Nigeria

Victor A. Okhuese, Oduwole Henry Kehinde
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Abstract

This paper focuses on the development and analysis of the endemic model for disease control in an aged-structured population in Nigeria. Upon the model framework development, the model equations were transformed into proportions with rate of change of the different compartments forming the model, thereby reducing the model equations from twelve to ten homogenous ordinary differential equations. The model exhibits two equilibria, the endemic state and the disease-free equilibrium state while successfully achieving a Reproductive Number R_0=0. The deterministic endemic susceptible-exposed-infected-removed-undetectable=untransmissible-susceptible (SEIRUS) model is analyzed for the existence and stability of the disease-free equilibrium state. We established that a disease-free equilibrium state exists and is locally asymptotically stable when the basic reproduction number 0≤R_0<1. Furthermore, numerical simulations were carried to complement the analytical results in investigating the effect treatment rate and the net transmission rate on recovery for both juvenile and adult sub-population in an age-structured population.
年龄结构确定性地方性疾病控制模型在尼日利亚的应用
本文的重点是发展和分析地方病模型的疾病控制在一个年龄结构的人口在尼日利亚。随着模型框架的发展,将模型方程转化为组成模型的不同隔室的变化率比例,从而将模型方程从12个齐次常微分方程减少到10个。该模型在成功实现繁殖数R_0=0的情况下,呈现出地方性和无病平衡状态。分析了确定性流行易感-暴露-感染-移除-检测不到=不传播-易感(SEIRUS)模型的无病平衡状态的存在性和稳定性。证明了当基本繁殖数0≤R_0<1时,存在无病平衡状态,且该状态局部渐近稳定。此外,通过数值模拟研究了处理率和净传播率对年龄结构种群中少年亚种群和成年亚种群恢复的影响,以补充分析结果。
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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