A stage-structured SEIR model with time-dependent delays in an almost periodic environment

Mathematical Biosciences and Engineering

卷:17

Lizhong Qiang¹  Zhi-Cheng Wang²  Ren-Hu Wang²  Ruofan An³ 

[1] 1. College of Mathematics and Statistics, Northwest Normal University, Lanzhou, Gansu 730070, P. R. China;

[2] 2. School of Mathematics and Statistics, Lanzhou University, Lanzhou, Gansu 730000, P. R. China;

[3] 3. School of Mathematics, China University of Mining and Technology, Xuzhou, Jiangsu 221008, P. R. China;

关键词: almost periodicity;    seir model;    time-dependent delay;    basic reproduction ratio;    threshold dynamics;   

DOI  :  10.3934/mbe.2020393

来源: DOAJ

【 摘 要 】

In this paper, we propose and investigate an almost periodic SEIR model with stage structure and latency, in which time-dependent maturation and incubation periods are incorporated. Two threshold parameters for the persistence and extinction of population and disease are introduced: the basic reproduction ratio $\hat{R}_{0}$ for population and the basic reproduction ratio $R_{0}$ for disease. If $\hat{R}_{0}<1$, the population extinction state is globally attractive. In the case where $\hat{R}_{0}>1$, it is shown that the disease tends to die out if $R_{0}<1$, while remains persistent if $R_{0}>1$. By virtue of numerical simulations, we verify the analytic results and investigate the effects of the fluctuations of maturation and incubation periods on disease transmission.

【 授权许可】

Unknown