Global results for an SIRS model with vaccination and isolation

DOI10.1016/j.nonrwa.2010.05.009zbMath1206.34069OpenAlexW2030489368MaRDI QIDQ708587

Chengjun Sun, Wei Yang

Publication date: 14 October 2010

Published in: Nonlinear Analysis. Real World Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.nonrwa.2010.05.009

zbMATH Keywords

bifurcationglobal stabilityuniform persistenceepidemiologyvaccinationisolation

Mathematics Subject Classification ID

Epidemiology (92D30) Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Bifurcation theory for ordinary differential equations (34C23) Stability of solutions to ordinary differential equations (34D20) Qualitative investigation and simulation of ordinary differential equation models (34C60) Asymptotic properties of solutions to ordinary differential equations (34D05)

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Cites Work

• Unnamed Item
• Unnamed Item
• Final and peak epidemic sizes for \(SEIR\) models with quarantine and isolation
• Backward bifurcation of an epidemic model with standard incidence rate and treatment rate
• Influence of nonlinear incidence rates upon the behavior of SIRS epidemiological models
• A simple vaccination model with multiple endemic states
• Homoclinic bifurcation in an SIQR model for childhood diseases
• Global dynamics of a SEIR model with varying total population size
• Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission
• Effects of quarantine in six endemic models for infectious diseases
• Backward bifurcations in simple vaccination models
• Recurrent outbreaks of childhood diseases revisited: The impact of isolation
• An SVEIR model for assessing potential impact of an imperfect anti-SARS vaccine
• The Mathematics of Infectious Diseases
• Global Dynamics of an SEIR Epidemic Model with Vertical Transmission
• Uniformly Persistent Systems
• Some applications of Hausdorff dimension inequalities for ordinary differential equations
• Additive compound matrices and an inequality for eigenvalues of symmetric stochastic matrices
• The Spread and Quarantine of HIV Infection in a Prison System
• Global Results for an Epidemic Model with Vaccination that Exhibits Backward Bifurcation
• A Geometric Approach to Global-Stability Problems
• Dynamical systems in population biology

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