Global Stability of a Vaccination Model with Immigration
نویسندگان
چکیده
We study an SV IR model of disease transmission with immigration into all four classes. Vaccinated individuals may only receive partial immunity to the disease, giving a leaky vaccine. The incidence function permits a nonlinear response to the number of infectives, so that mass action and saturating incidence are included as special cases. Because of the immigration of infected individuals, there is no disease-free equilibrium and hence no basic reproduction number. We use the Brouwer Fixed Point Theorem to show that an endemic equilibrium exists and the Poincaré-Hopf Theorem to show that it is unique. We show the equilibrium is globally asymptotically stable by using a Lyapunov function.
منابع مشابه
Stability Analysis and Optimal Control of Vaccination and Treatment of a SIR Epidemiological Deterministic Model with Relapse
In this paper, we studied and formulated the relapsed SIR model of a constant size population with standard incidence rate. Also, the optimal control problem with treatment and vaccination as controls, subject to the model is formulated. The analysis carried out on the model, clearly showed that the infection free steady state is globally asymptotically stable if the bas...
متن کاملStability analysis of the transmission dynamics of an HBV model
Hepatitis B virus (HBV) infection is a major public health problem in the world today. A mathematical model is formulated to describe the spread of hepatitis B, which can be controlled by vaccination as well as treatment. We study the dynamical behavior of the system with fixed control for both vaccination and treatment. The results shows that the dynamics of the model is completely de...
متن کاملPermanence and global asymptotic stability of a delayed predator-prey model with Hassell-Varley type functional response
Here, a predator-prey model with Hassell-Varley type functional responses is studied. Some sufficient conditions are obtained for the permanence and global asymptotic stability of the system by using comparison theorem and constructing a suitable Lyapunov functional. Moreover, an example is illustrated to verify the results by simulation.
متن کاملAIDS Epidemic Modeling With Different Demographic Structures
The most urgent public health problem today is to devise effective strategies to minimize the destruction caused by the AIDS epidemic. Mathematical models based on the underlying transmission mechanisms of the AIDS virus can help the medical/scientific community understand and anticipate its spread in different populations and evaluate the potential effectiveness of different approaches for bri...
متن کاملGlobal stability of an SEIR epidemic model with constant immigration q
An SEIR epidemic model with the infectious force in the latent (exposed), infected and recovered period is studied. It is assumed that susceptible and exposed individuals have constant immigration rates. The model exhibits a unique endemic state if the fraction p of infectious immigrants is positive. If the basic reproduction number R0 is greater than 1, sufficient conditions for the global sta...
متن کامل