Stability and bifurcation for a multiple-group model for the dynamics of HIV/AIDS transmission
SIAM Journal on Applied Mathematics
Hopf bifurcation in epidemic models with a latent period and nonpermanent immunity
Mathematical and Computer Modelling: An International Journal
Continuous and impulsive vaccination of SEIR epidemic models with saturation incidence rates
Mathematics and Computers in Simulation
Original article: The domain of attraction for the endemic equilibrium of an SIRS epidemic model
Mathematics and Computers in Simulation
Analysis and control of an SEIR epidemic system with nonlinear transmission rate
Mathematical and Computer Modelling: An International Journal
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This paper uses two SIRS type epidemiological models to examine the impact on the spread of disease caused by vaccination when the immunity gained from such an intervention is not lifelong. This occurs, for example, in vaccination against influenza. We assume that susceptible individuals become immune immediately after vaccination and that immune individuals become susceptible to infection after a sufficient lapse of time. In our first model, we consider a constant contact rate between infectious and susceptible individuals, whereas in our second model this depends on the current size of the population. The death rate in both models depends on population density. We examine the different types of dynamic and long term behaviour possible in our models and in particular examine the existence and stability of equilibrium solutions. We find that Hopf bifurcation is theoretically possible but appears not to occur for realistic parameter values. Numerical simulations confirm the analytical results. The paper concludes with a brief discussion.