Analysis of a fractional SIR model with general incidence function
type: Item
instance of: scholarly article
title: Analysis of a fractional SIR model with general incidence function
zbMATH Open document ID: 1451.92294
author: Pegah Taghiei Karaji
author: N. Nyamoradi
published in: Applied Mathematics Letters
publication date: 2020-10-08T00:00:00Z
review text: This paper presents a stability analysis for a fractional hepatitis B virus epidemic model. With \(S\), \(I\), \(R\) representing the susceptible, infectious, and recovered groups, the model featuring a general incidence function \(g(S,I)\) is given by \begin{align*} D^{\alpha}S(t)&=\lambda^{\alpha}-g(S,I)-(\mu_0^{\alpha}+\nu^{\alpha})S,\\ D^{\alpha}I(t)&=g(S,I)-(\mu_0^{\alpha}+\mu_1^{\alpha}+\beta^{\alpha})I,\text{ and }\\ D^{\alpha}R(t)&=\beta^{\alpha}I+\nu^{\alpha}S-\mu_0^{\alpha}R, \end{align*} where \(D^{\alpha}\) is the Caputo fractional derivative and the parameters are described as follows. The birth rate is \(\lambda\), the transmission rate of disease is \(\alpha\), the disease induced death rate and the natural death rate are \(\mu_1\) and \(\mu_0\) respectively, and the recovery rate is \(\beta\). Moreover, \(\nu\) is the vaccination rate. Under some conditions, the equilibrium points and the basic reproduction number \(R_0\) are derived for this model. It is shown that if \(R_0<1\) the disease-free equilibrium is locally asymptotically stable, and if \(R_0>1\) then this point is unstable. When \(R_0\le1\), the disease-free equilibrium of the system is shown to be globally asymptotically stable.
reviewed by: Yilun Shang
Mathematics Subject Classification ID: 92D30
Mathematics Subject Classification ID: 34D23
Mathematics Subject Classification ID: 26A33
zbMATH DE Number: 7258062
zbMATH Keywords: hepatitis B
zbMATH Keywords: stability
zbMATH Keywords: fractional Barbalat's lemma
zbMATH Keywords: basic reproduction number
zbMATH Keywords: fractional differential equations
MaRDI profile type: Publication
full work available at URL: j.aml.2020.106499
OpenAlex ID: W3030736352
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DOI: 10.1016/J.AML.2020.106499
description: scientific article; zbMATH DE number 7258062