时滞微分方程
基本再生数
延迟(音频)
数学
理论(学习稳定性)
流行病模型
繁殖
微分方程
拉伤
应用数学
控制理论(社会学)
数学分析
生物
计算机科学
医学
电信
控制(管理)
人口
人工智能
机器学习
解剖
环境卫生
生态学
作者
Masoud Saade,Samiran Ghosh,Malay Banerjee,Vitaly Volpert
标识
DOI:10.1016/j.mbs.2024.109155
摘要
We propose new single and two-strain epidemic models represented by systems of delay differential equations and based on the number of newly exposed individuals. Transitions between exposed, infectious, recovered, and back to susceptible compartments are determined by the corresponding time delays. Existence and positiveness of solutions are proved. Reduction of delay differential equations to integral equations allows the analysis of stationary solutions and their stability. In the case of two strains, they compete with each other, and the strain with a larger individual basic reproduction number dominates the other one. However, if the basic reproduction number exceeds some critical values, stationary solution loses its stability resulting in periodic time oscillations. In this case, both strains are present and their dynamics is not completely determined by the basic reproduction numbers but also by other parameters. The results of the work are illustrated by comparison with data on seasonal influenza.
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