登革热、基孔肯雅热和寨卡病毒动态传播的初步数学模型
A Preliminary Mathematical Model for the Dynamic Transmission of Dengue, Chikungunya and Zika
摘要：
埃及伊蚊是登革热、基孔肯雅热和寨卡病毒的已知传播媒介，本研究的目标是提出第一个数学模型来描述这三种疾病的动态传播。我们提出了两个初步模型，包括用于人群的SEIR模型和用于载体的SEI模型，以描述（a）登革热，基孔肯雅病毒或寨卡病毒的单一传播动态，以及（b）同一人群中两种疾病之间任何可能的合并感染。为了做到这一点，我们分别获得了每个模型的17和30个耦合微分方程系统的解析解，然后通过分析雅可比矩阵来获得特征值，以便开始开发预防这三种疾病传播的监测系统。
英文摘要：
Aedes aegypti is a known vector of Dengue, Chikungunya and Zika and the goal of this study is to propose the first mathematical model to describe the dynamic transmission of these three diseases. We present two preliminary models that consist of the SEIR model for the human populations and an SEI model for the vector to describe (a) the single transmission dynamics of dengue, Chikungunya or Zika, and (b) any possible coinfection between two diseases in the same population. In order to do that, we obtain an analytical solution of the system of 17 and 30 coupled differential equations for each model respectively, and later obtain the eigenvalues by analyzing the Jacobian matrix in order to begin the development of a surveillance system to prevent the spread of these three diseases.
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