Global stability of an SEIR epidemic model with constant immigration q
نویسندگان
چکیده
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 stability of the endemic equilibrium are obtained by the compound matrix theory. 2005 Elsevier Ltd. All rights reserved.
منابع مشابه
Global Dynamics of an Seir Epidemic Model with Immigration of Different Compartments
The SEIR epidemic model studied here includes constant inflows of new susceptibles, exposeds, infectives, and recovereds. This model also incorporates a population size dependent contact rate and a disease-related death. As the infected fraction cannot be eliminated from the population, this kind of model has only the unique endemic equilibrium that is globally asymptotically stable. Under the ...
متن کاملDynamics of a Delayed Epidemic Model with Beddington-DeAngelis Incidence Rate and a Constant Infectious Period
In this paper, an SIR epidemic model with an infectious period and a non-linear Beddington-DeAngelis type incidence rate function is considered. The dynamics of this model depend on the reproduction number R0. Accurately, if R0 < 1, we show the global asymptotic stability of the disease-free equilibrium by analyzing the corresponding characteristic equation and using compa...
متن کاملA lyapunov function and global properties for sir and seir epidemiological models with nonlinear incidence.
Explicit Lyapunov functions for SIR and SEIR compartmental epidemic models with nonlinear incidence of the form betaI(p)S(q) for the case p </= 1 are constructed. Global stability of the models is thereby established.
متن کاملOn stability and bifurcation of solutions of an SEIR epidemic model with vertical transmission
A four-dimensional SEIR epidemic model is considered. The stability of the equilibria is established. Hopf bifurcation and center manifold theories are applied for a reduced three-dimensional epidemic model. The boundedness, dissipativity, persistence, global stability , and Hopf-Andronov-Poincaré bifurcation for the four-dimensional epidemic model are studied. 1. Introduction. Many infectious ...
متن کاملPersistence of an SEIR Model with Immigration Dependent on the Prevalence of Infection
We incorporate the immigration of susceptible individuals into an SEIR epidemic model, assuming that the immigration rate decreases as the spread of infection increases. For this model, the basic reproduction number, R0, is found, which determines that the disease is either extinct or persistent ultimately. The obtained results show that the disease becomes extinct as R0 < 1 and persists in the...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2006