Stability, bifurcation, and a pair of conserved quantities in a simple epidemic system with reinfection for the spread of diseases caused by coronaviruses
type: Item
instance of: scholarly article
title: Stability, bifurcation, and a pair of conserved quantities in a simple epidemic system with reinfection for the spread of diseases caused by coronaviruses
zbMATH Open document ID: 1486.92208
DOI: 10.1155/2021/1570463
author: Jorge Fernando Camacho
author: Cruz Vargas-De-León
published in: Discrete Dynamics in Nature and Society
publication date: 2021-12-13T00:00:00Z
review text: Summary: In this paper, we study a modified SIRI model without vital dynamics, based on a system of nonlinear ordinary differential equations, for epidemics that exhibit partial immunity after infection, reinfection, and disease-induced death. This model can be applied to study epidemics caused by SARS-CoV, MERS-CoV, and SARS-CoV-2 coronaviruses, since there is the possibility that, in diseases caused by these pathogens, individuals recovered from the infection have a decrease in their immunity and can be reinfected. On the other hand, it is known that, in populations infected by these coronaviruses, individuals with comorbidities or older people have significant mortality rates or deaths induced by the disease. By means of qualitative methods, we prove that such system has an endemic equilibrium and an infinite line of nonhyperbolic disease-free equilibria, we determine the local and global stability of these equilibria, and we also show that it has no periodic orbits. Furthermore, we calculate the basic reproductive number \(( R_0)\) and find that the system exhibits a forward bifurcation: disease-free equilibria are stable when \(R_0<1/\sigma\) and unstable when \(R_0>1/\sigma\), while the endemic equilibrium consist of an asymptotically stable upper branch that appears from \(R_0>1/\sigma\), \(\sigma\) being the rate that quantifies reinfection. We also show that this system has two conserved quantities. Additionally, we show some of the most representative numerical solutions of this system.
Mathematics Subject Classification ID: 92D30
zbMATH DE Number: 7443931
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2021/1570463
OpenAlex ID: W3216706798
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description: scientific article; zbMATH DE number 7443931