Hopf bifurcation in two SIRS density dependent epidemic models

DOI10.1016/j.mcm.2004.06.007zbMath1065.92042OpenAlexW2060704981MaRDI QIDQ1765048

Qamar Jalil Ahmed Khan, David Greenhalgh, Fraser Lewis

Publication date: 22 February 2005

Published in: Mathematical and Computer Modelling (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.mcm.2004.06.007

zbMATH Keywords

Hopf bifurcationSIRS epidemic modelsTime delayDensity dependenceImmunizationContact rates

Mathematics Subject Classification ID

Epidemiology (92D30) Probabilistic models, generic numerical methods in probability and statistics (65C20) Stability theory of functional-differential equations (34K20) Bifurcation theory of functional-differential equations (34K18)

Related Items (16)

Dynamics of SVEIS epidemic model with distinct incidence ⋮ Continuous and impulsive vaccination of SEIR epidemic models with saturation incidence rates ⋮ Mathematical model of SIR epidemic system (COVID-19) with fractional derivative: stability and numerical analysis ⋮ Optimal control strategies for an age‐structured SEIR epidemic model ⋮ Wave propagation in a diffusive epidemic model with demography and time-periodic coefficients ⋮ Asymmetry in the presence of migration stabilizes multistrain disease outbreaks ⋮ Successive vaccination and difference in immunity of a delay SIR model with a general incidence rate ⋮ A stochastic SIRS epidemic model with infectious force under intervention strategies ⋮ A study of a diseased prey-predator model with refuge in prey and harvesting from predator ⋮ Persistence and extinction of disease in non-autonomous SIRS epidemic models with disease-induced mortality ⋮ Analysis and control of an SEIR epidemic system with nonlinear transmission rate ⋮ An SIRS epidemic model incorporating media coverage with time delay ⋮ The domain of attraction for the endemic equilibrium of an SIRS epidemic model ⋮ Singular perturbation approach to stability of a SIRS epidemic system ⋮ Stability and Hopf bifurcation for a delayed SIR epidemic model with logistic growth ⋮ Stability of Hopf bifurcation of a delayed SIRS epidemic model with stage structure

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Evaluation of age-specific vaccination strategies
• Population models for diseases with no recovery
• Patterns in the effects of infectious diseases on population growth
• Analytical threshold and stability results on age-structured epidemic models with vaccination
• Possible demographic consequences of HIV/AIDS epidemics. I. Assuming HIV infection always leads to AIDS
• Heterogeneity in disease-transmission modeling
• Disease in changing populations: Growth and disequilibrium
• Dynamic models of infectious diseases as regulators of population sizes
• Disease transmission models with density-dependent demographics
• Vaccination in density-dependent epidemic models
• Epidemic and demographic interaction in the spread of potentially fatal diseases in growing populations
• The Hopf bifurcation and its applications. With contributions by P. Chernoff, G. Childs, S. Chow, J. R. Dorroh, J. Guckenheimer, L. Howard, N. Kopell, O. Lanford, J. Mallet-Paret, G. Oster, O. Ruiz, S. Schecter, D. Schmidt, and S. Smale
• Modeling and analyzing HIV transmission: The effect of contact patterns
• Hopf bifurcation in epidemic models with a latent period and nonpermanent immunity
• The saturating contact rate in marriage- and epidemic models
• Modelling epidemics with variable contact rates
• Analysis of a disease transmission model in a population with varying size
• Models for the spread of universally fatal diseases
• Vaccination campaigns for common childhood diseases
• Deterministic models for common childhood diseases
• Stability and Bifurcation for a Multiple-Group Model for the Dynamics of HIV/AIDS Transmission
• Existence, threshold and stability results for an age-structured epidemic model with vaccination and a non-separable transmission coefficient

This page was built for publication: Hopf bifurcation in two SIRS density dependent epidemic models