Extinction and permanence of a general non-autonomous discrete-time SIRS epidemic model

Butsayapat Chaihao; Sujin Khomrutai; Butsayapat Chaihao; Sujin Khomrutai

doi:10.3934/math.2023486

AIMS Mathematics

2023, Volume 8, Issue 4: 9624-9646. doi: 10.3934/math.2023486

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Research article

Extinction and permanence of a general non-autonomous discrete-time SIRS epidemic model

Butsayapat Chaihao ,
Sujin Khomrutai ^,

Department of Mathematics and Computer Science, Faculty of Science, Chulalongkorn University, Bangkok 10330, Thailand

Received: 07 November 2022 Revised: 05 February 2023 Accepted: 06 February 2023 Published: 20 February 2023
MSC : 34D05, 34D23, 92D30

We investigate a non-autonomous discrete-time SIRS epidemic model with nonlinear incidence rate and distributed delays combined with a nonlinear recovery rate taken into account the impact of health care resources. Two threshold parameters $ \mathcal{R}_0, \mathcal{R}_\infty $ are obtained so that the disease dies out when $ \mathcal{R}_0 < 1 $; and the infective persists indefinitely when $ \mathcal{R}_\infty > 1 $.
- non-autonomous SIRS model,
- threshold parameters,
- extinction,
- permanence,
- number of hospital beds
Citation: Butsayapat Chaihao, Sujin Khomrutai. Extinction and permanence of a general non-autonomous discrete-time SIRS epidemic model[J]. AIMS Mathematics, 2023, 8(4): 9624-9646. doi: 10.3934/math.2023486

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Abstract

We investigate a non-autonomous discrete-time SIRS epidemic model with nonlinear incidence rate and distributed delays combined with a nonlinear recovery rate taken into account the impact of health care resources. Two threshold parameters $ \mathcal{R}_0, \mathcal{R}_\infty $ are obtained so that the disease dies out when $ \mathcal{R}_0 < 1 $; and the infective persists indefinitely when $ \mathcal{R}_\infty > 1 $.

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