On the backward bifurcation of a vaccination model with nonlinear incidence
نویسندگان
چکیده
Abstract. A compartmental epidemic model, introduced by Gumel and Moghadas [1], is considered. The model incorporates a nonlinear incidence rate and an imperfect preventive vaccine given to susceptible individuals. A bifurcation analysis is performed by applying the bifurcation method introduced in [2], which is based on the use of the center manifold theory. Conditions ensuring the occurrence of backward bifurcation are derived. The obtained results are numerically validated and then discussed from both the mathematical and the epidemiological perspective.
منابع مشابه
Stability and Bifurcation of an SIS Epidemic Model with Saturated Incidence Rate and Treatment Function
In this paper an SIS epidemic model with saturated incidence rate and treatment func- tion is proposed and studied. The existence of all feasible equilibrium points is discussed. The local stability conditions of the disease free equilibrium point and endemic equilibrium point are established with the help of basic reproduction number.However the global stabili- ty conditions of these eq...
متن کاملAnalysis of stability and bifurcation for an SEIV epidemic model with vaccination and nonlinear incidence rate
In this paper, an SEIV epidemic model with vaccination and nonlinear incidence rate is formulated. The analysis of the model is presented in terms of the basic reproduction number R0. It is shown that the model has multiple equilibria and using the center manifold theory, the model exhibits the phenomenon of backward bifurcation where a stable diseasefree equilibrium coexists with a stable ende...
متن کاملAnalysis of SIR epidemic models with nonlinear incidence rate and treatment.
This paper deals with the nonlinear dynamics of a susceptible-infectious-recovered (SIR) epidemic model with nonlinear incidence rate, vertical transmission, vaccination for the newborns of susceptible and recovered individuals, and the capacity of treatment. It is assumed that the treatment rate is proportional to the number of infectives when it is below the capacity and constant when the num...
متن کاملOn the study of an SEIV epidemic model concerning vaccination and vertical transmission
In this work, we study an epidemic model with vaccination and vertical transmission. We get the basic reproduction number R0 of the system and carry out a bifurcation analysis and obtain the conditions ensuring that the system exhibits backward bifurcation. Mathematics Subject Classification : 34C05, 92D25
متن کاملBifurcation in a variational problem on a surface with a constraint
We describe a variational problem on a surface under a constraintof geometrical character. Necessary and sufficient conditions for the existence ofbifurcation points are provided. In local coordinates the problem corresponds toa quasilinear elliptic boundary value problem. The problem can be consideredas a physical model for several applications referring to continuum medium andmembranes.
متن کامل