Global dynamics of an SI epidemic model with nonlinear incidence rate, feedback controls and time delays

Ke Guo; Wanbiao Ma; Ke Guo; Wanbiao Ma

doi:10.3934/mbe.2021035

Mathematical Biosciences and Engineering

2021, Volume 18, Issue 1: 643-672. doi: 10.3934/mbe.2021035

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Global dynamics of an SI epidemic model with nonlinear incidence rate, feedback controls and time delays

Ke Guo ,
Wanbiao Ma ^,

School of Mathematics and Physics, University of Science and Technology Beijing, Beijing 100083, China

Received: 16 August 2020 Accepted: 01 December 2020 Published: 15 December 2020

In this paper, we consider a class of SI epidemic model with nonlinear incidence, feedback controls and four different discrete time delays. By skillfully constructing appropriate Lyapunov functionals, and combining Lyapunov-LaSalle invariance principle and Barbalat's lemma, the global dynamics of the model are established. Our results extend and improve related works in the existing literatures.
- SI epidemic model,
- feedback control,
- time delay,
- Lyapunov functional,
- global stability
Citation: Ke Guo, Wanbiao Ma. Global dynamics of an SI epidemic model with nonlinear incidence rate, feedback controls and time delays[J]. Mathematical Biosciences and Engineering, 2021, 18(1): 643-672. doi: 10.3934/mbe.2021035

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Abstract

In this paper, we consider a class of SI epidemic model with nonlinear incidence, feedback controls and four different discrete time delays. By skillfully constructing appropriate Lyapunov functionals, and combining Lyapunov-LaSalle invariance principle and Barbalat's lemma, the global dynamics of the model are established. Our results extend and improve related works in the existing literatures.

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