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Computation of periodic solutions to models of infectious disease dynamics and immune response
Russian Journal of Numerical Analysis and Mathematical Modelling ( IF 0.6 ) Pub Date : 2021-04-01 , DOI: 10.1515/rnam-2021-0008
M. Yu. Khristichenko 1, 2 , Yu. M. Nechepurenko 2, 3
Affiliation  

The paper is focused on computation of stable periodic solutions to systems of delay differential equations modelling the dynamics of infectious diseases and immune response. The method proposed here is described by an example of the well-known model of dynamics of experimental infection caused by lymphocytic choriomeningitis viruses. It includes the relaxation method for forming an approximate periodic solution, a method for estimating the approximate period of this solution based on the Fourier series expansion, and a Newton-type method for refining the approximate period and periodic solution. The results of numerical experiments are presented and discussed. The proposed method is compared to known ones.

中文翻译:

传染病动力学和免疫反应模型的周期解的计算

本文的重点是对延迟微分方程系统的稳定周期解的计算,该系统对传染病和免疫反应的动力学进行建模。这里提出的方法是由淋巴细胞脉络膜脑膜炎病毒引起的实验性感染动力学的众所周知的模型的一个例子来描述的。它包括用于形成近似周期解的松弛方法,基于傅立叶级数展开估计该解的近似周期的方法以及用于细化近似周期和周期解的牛顿型方法。提出并讨论了数值实验的结果。将所提出的方法与已知方法进行比较。
更新日期:2021-04-14
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