Mathematical modeling of chickenpox transmission using the Laplace Adomian Decomposition Method

Q3 Mathematics

Results in Control and Optimization Pub Date : 2024-06-01 DOI:10.1016/j.rico.2024.100436

Tawakalt A. Ayoola, Amos O. Popoola, Morufu O. Olayiwola, Adedapo I. Alaje

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Abstract

In this work, mathematical modeling of a nonlinear differential equation was studied to investigate the effect of vaccination on the spread of chickenpox. The proof of existence and uniqueness of the positive solution and invariant region showed that the model is epidemiologically sound. We established the disease-free and endemic equilibrium states and carried out a stability analysis of the disease-free and endemic equilibrium states of the model to gain insight into the dynamics of the model. The rate of vaccination and precaution for the spread of chickenpox was a factor that influenced the basic reproductive number, which was calculated using the next-generation matrix approach. Forecasts made via numerical simulation using the Laplace Adomian Decomposition method highlight the temporal impact of vaccination on curbing the chicken pox trend.

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利用拉普拉斯-阿多米安分解法建立水痘传播的数学模型

在这项工作中，我们研究了一个非线性微分方程的数学模型，以探讨接种疫苗对水痘传播的影响。正解和不变区的存在性和唯一性证明，该模型在流行病学上是合理的。我们建立了模型的无病平衡态和流行平衡态，并对模型的无病平衡态和流行平衡态进行了稳定性分析，从而深入了解了模型的动力学特性。疫苗接种率和水痘传播的预防率是影响基本繁殖数的一个因素，基本繁殖数是通过下一代矩阵法计算得出的。利用拉普拉斯-阿多米安分解法进行的数值模拟预测突出了疫苗接种对遏制水痘趋势的时间影响。

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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