MATHEMATICAL MODEL OF MEASLES DISEASE SPREAD WITH TWO-DOSE VACCINATION AND TREATMENT

Journal of Fundamental Mathematics and Applications (JFMA) Pub Date : 2023-11-27 DOI:10.14710/jfma.v6i2.20091

Muhammad Manaqib, Ayu Kinasih Yuliawati, Dhea Urfina Zulkifli

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Abstract

This study developed a model for the spread of measles based on the SEIR model by adding the factors of using the first dose of vaccination, the second dose of vaccination, and treatment. Making this model begins with making a compartment diagram of the spread of the disease, which consists of seven subpopulations, namely susceptible subpopulations, subpopulations that have received the first dose of vaccination, subpopulations that have received the second dose vaccination, exposed subpopulations, infected subpopulations, subpopulations that have received treatment, and subpopulations healed. After the model is formed, the disease-free equilibrium point, endemic equilibrium point, and basic reproduction number (R_0) are obtained. Analysis of the stability of the disease-for equilibrium point was locally asymptotically stable when (R_0)<1. The backward bifurcation analysis occurs when (R_C) is present and R_C

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使用两剂疫苗接种和治疗的麻疹疾病传播数学模型

本研究在 SEIR 模型的基础上，通过添加使用第一剂疫苗、第二剂疫苗和治疗等因素，建立了麻疹传播模型。制作该模型首先要制作疾病传播的分区图，其中包括七个亚群，即易感亚群、接种第一剂疫苗的亚群、接种第二剂疫苗的亚群、暴露亚群、感染亚群、接受治疗的亚群和痊愈亚群。模型形成后，可得到无病平衡点、流行平衡点和基本繁殖数（R_0）。分析发现，当（R_0）<1 时，无病平衡点局部渐近稳定；当（R_C）出现且 R_C

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Journal of Fundamental Mathematics and Applications (JFMA)

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