Modeling and Analysis of an SEIRS Epidemic Model with Non-monotonic Incidence Rate (original) (raw)
Stability Analysis of SEIRS Epidemic Model with Nonlinear Incidence Rate Function
Mathematics
This paper addresses the global stability analysis of the SEIRS epidemic model with a nonlinear incidence rate function according to the Lyapunov functions and Volterra-Lyapunov matrices. By creating special conditions and using the properties of Volterra-Lyapunov matrices, it is possible to recognize the stability of the endemic equilibrium (E1) for the SEIRS model. Numerical results are used to verify the presented analysis.
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 Analysis of a SEIR EpidemicModel with Saturation Incidence Rate
2014
The global stability of a SEIR epidemic model with saturating incidence rate is investigated. A threshold R 0 is identified which determines the outcome of the disease. If 1 0 R , the infected fraction of the population disappears and the disease dies out while if 1 0 R , the infected fraction persists and a unique equilibrium state is shown under a careful restriction of parameters. Dulac's criterion plus Poincare'-Bendixson theorem and Lyapunov functions are used to prove the global stability of the disease free and endemic equilibria respectively. Numericalsimulation illustrates the main results in the paper.
Modeling and Analysis of an SEIRS Epidemic Model with Saturated Incidence
In this paper, an SEIRS epidemic model with nonlinear incidence rate is investigated. The model exhibits two equilibria namely, the disease-free equilibrium and the endemic equilibrium. It is shown that if the basic reproduction number, R 0 <1 the disease free equilibrium is locally and globally asymptotically stable. Also, we show that R 0 >1, the disease equilibrium is locally asymptotically stable and the disease is uniformly persisted. Some numerical simulations are given to illustrate the analytical results.
Stability Analysis of a SEIV Epidemic Model with Saturated Incidence Rate
British Journal of Mathematics & Computer Science, 2014
In this paper, a SEIV epidemic model with saturated incidence rate that incorporates polynomial information on current and past states of the disease is investigated. The model exhibits two equilibria, disease-free equilibrium (DFE) and the endemic equilibrium (EE). It is shown that if the basic reproduction number, R 0 < 1, the DFE is locally asymptotically stable and by the use of Lyapunov function, DFE is globally asymptotically stable and in such a case, the EE is unstable. Moreover, if R 0 >1, the endemic equilibrium is locally asymptotically stable. The effects of the rate at which vaccine wanes (ω) are investigated through numerical stimulations.
Stability analysis of an SVIR epidemic model with non-linear saturated incidence rate
Applied Mathematical Sciences, 2015
In this paper, we present an SVIR epidemic model with non-linear saturated incidence rate. Initially the basic formulation of the model is presented. Two equilibrium point exists for the system; disease free and endemic equilibrium. The stability of the disease free and endemic equilibrium exists when the basic reproduction less or greater than unity, respectively. If the value of R 0 , less then one then the disease free equilibrium is locally as well as globally asymptotically stable, and if its exceeds, the endemic equilibrium is stable both locally and globally. The numerical results are presented for illustration.
Dynamics of an SEIR epidemic model with nonlinear incidence and treatment rates
Nonlinear Dynamics, 2019
The control of highly contagious diseases is very important today. In this paper, we proposed an SEIR model with Crowley-Martin-type incidence rate and Holling type II and III treatment rates. Dynamics of the spread of infection and its control are performed for both the cases of treatment functions. We have performed the stability and bifurcation analyses of the model system. The sensitivity analysis of all the parameters with respect to the basic reproduction number has been performed. Furthermore, we discussed the optimal control strategy using Pontryagin's maximum principle and determined the effect of control parameter u on the model dynamics. Moreover, we validate the theoretical results using numerical simulations. Between both the treatment functions, we observe that the implementation of Holling type II treatment is most effective to prevent the spread of diseases. Thus, we conclude that the pervasive effect of treatment not only
Analysis of a SEIV epidemic model with a nonlinear incidence rate
Applied Mathematical Modelling, 2009
In this paper, a SEIV epidemic model with a nonlinear incidence rate is investigated. The model exhibits two equilibria, namely, the disease-free equilibrium and the endemic equilibrium. It is shown that if the basic reproduction number R 0 < 1, the disease-free equilibrium is globally asymptotically stable and in such a case the endemic equilibrium does not exist. Moreover, we show that if the basic reproduction number R 0 > 1, the disease is uniformly persistent and the unique endemic equilibrium of the system with saturation incidence is globally asymptotically stable under certain conditions.
Global stability analysis of an SEIR epidemic model with vertical transmission
International Journal of Dynamical Systems and Differential Equations, 2017
The aim of this paper is to include general incidence function in the SEIR epidemic model with both horizontal and vertical transmission. We focus on the global stability of all possible equilibria: the disease-free equilibrium and the endemic equilibrium. The global stability of the disease-free equilibrium is proved by constructing a suitable Lyapunov function and under some appropriate assumptions on the incidence function, the global dynamics of the endemic equilibrium is determined by the geometric approach.