Age Structured Deterministic Model of Diphtheria Infection

E. S. Udofia, Ubong D. Akpan, Joy Ijeoma Uwakwe, Henry Sylvester Thomas
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Abstract

Age-structured mathematical model of diphtheria infection has been formulated with specific epidemiological classes such as S1, susceptible infant at time t (0-1years), S2, susceptible school children population at time t, V, vaccination population at time t, E, exposed population at time t, I1, asymptomatic infection population at time t, I2, symptomatic infection population at time t, ID, detected infectious humans at time t (asymptomatic and symptomatic) population through testing, R, recovered population at time t. It was established through theorems and proofs that the model is epidemiologically meaningful, and that all its state variables are positive (non-negative) at time t>0 in the domain ℘, and that the domain ℘ is indeed bounded. Using the next generation matrix, the reproduction ratio Rb of the system was determined. Using dynamical system theory, it was established that the system is locally stable. A matrix-theoretic method was used in the construction of an appropriate Lyapunov function for the global stability analysis of the formulated model, and also established that the system is globally asymptotically stable if Rb≤1 and unstable otherwise.
白喉感染的年龄结构决定论模型
白喉感染的年龄结构数学模型具有特定的流行病学类别,如 S1,t 时的易感婴儿(0-1 岁);S2,t 时的学龄儿童易感人群;V,t 时的疫苗接种人群;E,t 时的暴露人群;I1,t 时的无症状感染人群;I2,t 时的有症状感染人群;ID,t 时通过检测发现的感染人群(无症状和有症状);R,t 时的康复人群。通过定理和证明,可以确定该模型在流行病学上是有意义的,其所有状态变量在时间 t>0 时在域℘内均为正(非负),且域℘确实是有界的。利用下一代矩阵,确定了系统的繁殖率 Rb。利用动力系统理论,确定了系统的局部稳定性。利用矩阵理论方法构建了适当的 Lyapunov 函数,用于对所建模型进行全局稳定性分析,并确定如果 Rb≤1 则系统全局渐近稳定,否则不稳定。
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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