Mathematical analysis of a general two-patch model of tuberculosis disease with lost sight individuals
type: Item
instance of: scholarly article
title: Mathematical analysis of a general two-patch model of tuberculosis disease with lost sight individuals
zbMATH Open document ID: 1406.92586
DOI: 10.1155/2014/263780
author: Abdias Laohombé
author: Isabelle Ngningone Eya
author: Alassane Bah
author: Samuel Bowong
author: S. C. Oukouomi Noutchie
author: Jean Jules Tewa
published in: Abstract and Applied Analysis
publication date: 2019-02-14T00:00:00Z
review text: Summary: A two-patch model, \(S E_{i 1},\ldots, E_{i n} I_i L_i\), \(i = 1,2\), is used to analyze the spread of tuberculosis, with an arbitrary number \(n\) of latently infected compartments in each patch. A fraction of infectious individuals that begun their treatment will not return to the hospital for the examination of sputum. This fact usually occurs in sub-Saharan Africa, due to many reasons. The model incorporates migrations from one patch to another. The existence and uniqueness of the associated equilibria are discussed. A Lyapunov function is used to show that when the basic reproduction ratio is less than one, the disease-free equilibrium is globally and asymptotically stable. When it is greater than one, there exists at least one endemic equilibrium. The local stability of endemic equilibria can be illustrated using numerical simulations. Numerical simulation results are provided to illustrate the theoretical results and analyze the influence of lost sight individuals.
Mathematics Subject Classification ID: 92D30
Mathematics Subject Classification ID: 34D23
zbMATH DE Number: 7022043
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2014/263780
OpenAlex ID: W2143239825
Wikidata QID: Q59037288
cites work: Q4039920
cites work: Nonlinear differential equations and dynamical systems
cites work: Q5766570
cites work: On R. A. Smith's autonomous convergence theorem
cites work: A Geometric Approach to Global-Stability Problems
cites work: Global stability of SEIRS models in epidemiology
cites work: Global dynamics of an SEIR epidemic model with vertical transmission
cites work: Global analysis of two tuberculosis models
cites work: Global analysis of competition for perfectly substitutable resources with linear response
cites work: An SVEIR model for assessing potential impact of an imperfect anti-SARS vaccine
cites work: Two-Patch Transmission of Tuberculosis
cites work: Q4141027
cites work: Global Analysis of New Malaria Intrahost Models with a Competitive Exclusion Principle
cites work: Epidemiological models and Lyapunov functions
cites work: General models of host-parasite systems. Global analysis.
cites work: Global stability analysis for SEIS models with \(n\) latent classes
cites work: Global stability and persistence of simple food chains
cites work: Mathematical analysis of a tuberculosis model with differential infectivity
cites work: Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission
cites work: Mathematical analysis of a two-patch model of tuberculosis disease with staged progression
cites work: Approximate solution of tuberculosis disease population dynamics model
cites work: Solving a system of fractional partial differential equations arising in the model of HIV infection of \(\mathrm{CD4}^{+}\) cells and attractor one-dimensional Keller-Segel equations
Recommended article: Mathematical analysis of two-patch model for the dynamical transmission of tuberculosis
Recommended article: Analysis of a tuberculosis model with undetected and lost-sight cases
Recommended article: Mathematical analysis of a two-patch model of tuberculosis disease with staged progression
Recommended article: Global properties of a tuberculosis model with lost sight and multi-compartment of latents
Recommended article: Mathematical analysis of a tuberculosis model with differential infectivity
Recommended article: A mathematical analysis of a tuberculosis epidemic model with two treatments and exogenous re-infection
Recommended article: Mathematical analysis of a tuberculosis model with imperfect vaccine
Recommended article: Q4232415
Recommended article: Analysis of a mathematical model for tuberculosis with diagnosis
Recommended article: Q5267653
description: scientific article; zbMATH DE number 7022043