Analysis of stability and bifurcation for an SEIV epidemic model with vaccination and nonlinear incidence rate (original) (raw)
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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 ...
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Dynamical analysis of an epidemic model with saturated incidence rate and vaccination
An epidemic model with saturated incidence rate and vaccination is investigated. The model exhibits two equilibria namely disease-free and endemic equilibria. It is shown that if the basic reproduction number () 0 R is less than unity, the disease-free equilibrium is locally asymptotically stable and in such case, the endemic equilibrium does not exist. Also, it is shown that if 1 0 R , the disease is persistent and the unique endemic equilibrium of the system with saturation incidence is locally asymptotically stable. Lyapunov function and Dulac's criterion plus Poincare-Bendixson theorem are applied to prove the global stability of the disease-free and endemic equilibria respectively. The effect of vaccine in the model is critically looked into.
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This paper presents a two stage SIS epidemic model in animal population with bovine tuberculosis (BTB) in African buffalo as a guiding example. The proposed model is rigorously analyzed. The analysis reveals that the model exhibits the phenomenon of backward bifurcation, where a stable disease-free equilibrium (DFE) coexists with a stable endemic equilibrium (EE) when the associated reproduction number (R v) is less than unity. It is shown under two special cases of the presented model, that this phenomenon of backward bifurcation does not arise depending on vaccination coverage and efficacy of vaccine. Numerical simulations of the model show that, the use of an imperfect vaccine can lead to effective control of the disease if the vaccination coverage and the efficacy of vaccine are high enough.
Stability and bifurcation of an SIR epidemic model with nonlinear incidence and treatment
Applied Mathematics and Computation, 2009
The dynamical behaviors of an SIR epidemic model with nonlinear incidence and treatment is investigated. It is assumed that treatment rate is proportional to the number of infectives below the capacity and is a constant when the number of infectives is greater than the capacity. It is found that a backward bifurcation occurs if the capacity is small. It is also found that there exist bistable endemic equilibria if the capacity is low. Theoretical and numerical results suggest that decreasing the basic reproduction number below one is insufficient for disease eradication.
IOSR Journals , 2019
In this paper, we consider a SEIR epidemic model with homogenous transmission function and treatment. Found the basic reproduction number 0 R and equilibrium points namely disease-free equilibrium and endemic equilibrium. The global stability of the disease free equilibrium and endemic equilibrium is proved using Lyapunov function and Poincare-Bendixson theorem plus Dulac's criterion respectively and also study the sociological and psychological effect on the infected population. We gave some numerical result to analyze our model with actual model. MSC 2010: 34D20, 37B25, 93A30
Global Stability of Multi-Strain SEIR Epidemic Model with Vaccination Strategy
Mathematical and Computational Applications
A three-strain SEIR epidemic model with a vaccination strategy is suggested and studied in this work. This model is represented by a system of nine nonlinear ordinary differential equations that describe the interaction between susceptible individuals, strain-1-vaccinated individuals, strain-1-exposed individuals, strain-2-exposed individuals, strain-3-exposed individuals, strain-1-infected individuals, strain-2-infected individuals, strain-3-infected individuals, and recovered individuals. We start our analysis of this model by establishing the existence, positivity, and boundedness of all the solutions. In order to show global stability, the model has five equilibrium points: The first one stands for the disease-free equilibrium, the second stands for the strain-1 endemic equilibrium, the third one describes the strain-2 equilibrium, the fourth one represents the strain-3 equilibrium point, and the last one is called the total endemic equilibrium. We establish the global stability...