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

  • Received: 01 September 2020 Accepted: 22 October 2020 Published: 06 November 2020
  • 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.

    Citation: Lizhong Qiang, Ren-Hu Wang, Ruofan An, Zhi-Cheng Wang. A stage-structured SEIR model with time-dependent delays in an almost periodic environment[J]. Mathematical Biosciences and Engineering, 2020, 17(6): 7732-7750. doi: 10.3934/mbe.2020393

    Related Papers:

  • 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.


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