Dynamics of solutions of a diffusive time-delayed HIV/AIDS epidemic model: traveling wave solutions and spreading speeds
type: Item
instance of: scholarly article
title: Dynamics of solutions of a diffusive time-delayed HIV/AIDS epidemic model: traveling wave solutions and spreading speeds
zbMATH Open document ID: 1505.35079
author: Dawit Denu
author: Sedar Ngoma
author: Rachidi Bolaji Salako
published in: Journal of Differential Equations
publication date: 2022-11-28T00:00:00Z
review text: In this paper, the authors study a diffusive time-delayed HIV/AIDS epidemic model with information and education campaigns. The dynamics of classical solutions of the model is investigated, such as (i) disease's persistence and extinction, (ii) existence of epidemic waves, and (iii) spreading speeds. For (i), when the basic reproduction number is less than or equal to one, they show that the disease-free equilibrium solution is globally stable, and hence there is no epidemic wave in this case. However, if it is bigger than one, the disease will eventually persist. For (ii), they prove that there is a minimum wave speed such that the model has an endemic traveling wave solution connecting the disease-free equilibrium at the right end when the wave speed is greater than the minimum wave speed, and that there is no such traveling wave solution when the wave speed is less than the minimum wave speed. Moreover, they obtain that the minimum wave speed converges to \(0\) as the time-delay approaches infinity. For (iii), they study the disease spreading speeds interval and show that in the absence of time-delay, there is a single disease spreading speed, and this coincides with the minimal wave speed. The numerical simulations are presented to illustrate their theoretical results.
reviewed by: Guo-Bao Zhang
Mathematics Subject Classification ID: 35C07
Mathematics Subject Classification ID: 35B40
Mathematics Subject Classification ID: 35K45
Mathematics Subject Classification ID: 35K57
Mathematics Subject Classification ID: 92D30
zbMATH DE Number: 7624001
zbMATH Keywords: reaction-diffusion parabolic system
zbMATH Keywords: traveling waves
zbMATH Keywords: spreading speeds
zbMATH Keywords: time delay epidemic-model
describes a project that uses: diffEq
MaRDI profile type: Publication
full work available at URL: j.jde.2022.11.009
OpenAlex ID: W4309237050
cites work: Asymptotic profiles of the steady states for an SIS epidemic reaction-diffusion model
cites work: On the effect of lowering population's movement to control the spread of an infectious disease
cites work: Existence, uniqueness, and asymptotic stability of traveling waves in nonlocal evolution equations
cites work: Existence of traveling wave solutions of a deterministic vector-host epidemic model with direct transmission
cites work: Analysis of a time-delayed HIV/AIDS epidemic model with education campaigns
cites work: Spreading and vanishing in nonlinear diffusion problems with free boundaries
cites work: Qualitative analysis and travelling wave solutions for the SI model with vertical transmission
cites work: Traveling wavefronts for a two-species ratio-dependent predator-prey system with diffusion terms and stage structure
cites work: Traveling wavefronts for a two-species predator-prey system with diffusion terms and stage structure
cites work: Global stability for delay SIR and SEIR epidemic models with nonlinear incidence rate
cites work: Analysis of Newton's method to compute travelling waves in discrete media
cites work: Modeling the effect of information campaigns on the HIV epidemic in Uganda
cites work: Traveling waves for a nonlocal dispersal SIR model with delay and external supplies
cites work: Traveling wave solutions for delayed reaction-diffusion systems and applications to diffusive Lotka-Volterra competition models with distributed delays
cites work: Control strategies for a multi-strain epidemic model
cites work: Asymptotic properties of an HIV/AIDS model with a time delay
cites work: Modelling effects of public health educational campaigns on HIV/AIDS transmission dynamics
cites work: Time Delay ODE/PDE Models
cites work: A Compendium of Partial Differential Equation Models
cites work: Solving Differential Equations in R
cites work: Modelling the effect of treatment and behavioral change in HIV transmission dynamics
cites work: Traveling waves in a nonlocal dispersal SIR model with nonlocal delayed transmission
cites work: An Epidemic Model with Population Dispersal and Infection Period
cites work: Traveling waves of diffusive predator-prey systems: disease outbreak propagation
cites work: Travelling waves of a diffusive Kermack–McKendrick epidemic model with non-local delayed transmission
cites work: Theory and applications of partial functional differential equations
cites work: Traveling wave fronts of reaction-diffusion systems with delay
cites work: Q4243821
DOI: 10.1016/J.JDE.2022.11.009
description: scientific article; zbMATH DE number 7624001