We consider a family of periodic SEIRS epidemic models with a fairly general incidence rate of the form ( ), and it is shown that the basic reproduction number determines the global dynamics of the models and it is a threshold parameter for persistence of disease. Numerical simulations are performed using a nonlinear incidence rate to estimate the basic reproduction number and illustrate our analytical findings.
In this article, the clasical Bazykin model is modifed with Beddington-DeAngelis functional response, subject to self and cross-diffusion, in order to study the spatial dynamics of the model.We perform a detailed stability and Hopf bifurcation analysis of the spatial model system and determine the direction of Hopf bifurcation and stability of the bifurcating periodic solutions. We present some numerical simulations of time evolution of patterns to show the important role played by self and cross-diffusion as well as other parameters leading to complex patterns in the plane.
In this paper, we discussed a infinitely distributed delayed viral infection model with nonlinear immune response and general incidence rate. We proved the existence and uniqueness of the equilibria. By using the Lyapunov functional and LaSalle invariance principle, we obtained the conditions of global stabilities of the infection-free equilibrium, the immune-exhausted equilibrium and the endemic equilibrium. Numerical simulations are given to verify the analytical results.
We study the dynamics of a SIR epidemic model with nonlinear incidence rate, vertical transmission vaccination for the newborns and the capacity of treatment, that takes into account the limitedness of the medical resources and the efficiency of the supply of available medical resources. Under some conditions we prove the existence of backward bifurcation, the stability and the direction of Hopf bifurcation. We also explore how the mechanism of backward bifurcation affects the control of the infectious disease. Numerical simulations are presented to illustrate the theoretical findings.
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