Partial differential equations of an epidemic model with spatial diffusion
type: Item
instance of: scholarly article
title: Partial differential equations of an epidemic model with spatial diffusion
zbMATH Open document ID: 1300.92103
DOI: 10.1155/2014/186437
author: El Mehdi Lotfi
author: Mehdi Maziane
author: Khalid Hattaf
author: Noura Yousfi
published in: International Journal of Partial Differential Equations
publication date: 2014-09-30T00:00:00Z
review text: Summary: The aim of this paper is to study the dynamics of a reaction-diffusion SIR epidemic model with specific nonlinear incidence rate. The global existence, positivity, and boundedness of solutions for a reaction-diffusion system with homogeneous Neumann boundary conditions are proved. The local stability of the disease-free equilibrium and endemic equilibrium is obtained via characteristic equations. By means of Lyapunov functional, the global stability of both equilibria is investigated. More precisely, our results show that the disease-free equilibrium is globally asymptotically stable if the basic reproduction number is less than or equal to unity, which leads to the eradication of disease from population. When the basic reproduction number is greater than unity, then disease-free equilibrium becomes unstable and the endemic equilibrium is globally asymptotically stable; in this case the disease persists in the population. Numerical simulations are presented to illustrate our theoretical results.
Mathematics Subject Classification ID: 92D30
Mathematics Subject Classification ID: 35K57
Mathematics Subject Classification ID: 35B35
zbMATH DE Number: 6349582
zbMATH Keywords: reaction-diffusion SIR epidemic model
zbMATH Keywords: nonlinear incidence rate
zbMATH Keywords: global existence
zbMATH Keywords: boundedness
zbMATH Keywords: Neumann boundary
zbMATH Keywords: Lyapunov functional
Wikidata QID: Q59048813
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2014/186437
OpenAlex ID: W2078434836
cites work: On the dynamics of predator-prey models with the Beddington-DeAngelis functional response
cites work: GLOBAL STABILITY OF THE VIRAL DYNAMICS WITH CROWLEY-MARTIN FUNCTIONAL RESPONSE
cites work: Asymptotic properties of a stochastic predator-prey model with Crowley-Martin functional response
cites work: A delayed SIR epidemic model with a general incidence rate
cites work: Mathematical Structures of Epidemic Systems
cites work: Semigroups of linear operators and applications to partial differential equations
cites work: Q4746129
cites work: Q5533735
cites work: An application of the invariance principle to reaction diffusion equations
cites work: Global stability for reaction-diffusion equations in biology
cites work: Q4141027
description: scientific article; zbMATH DE number 6349582