scholarly journals Impulsive Vaccination SEIR Model with Nonlinear Incidence Rate and Time Delay

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Dongmei Li ◽  
Chunyu Gui ◽  
Xuefeng Luo
Keyword(s):  
Periodic Solution ◽  
Time Delay ◽  
Epidemic Model ◽  
Sufficient Conditions ◽  
Uniform Persistence ◽  
Nonlinear Incidence Rate ◽  
Constant Input ◽  
Seir Model ◽  
Nonlinear Incidence ◽  
Impulsive Vaccination

This paper aims to discuss the delay epidemic model with vertical transmission, constant input, and nonlinear incidence. Some sufficient conditions are given to guarantee the existence and global attractiveness of the infection-free periodic solution and the uniform persistence of the addressed model with time delay. Finally, a numerical example is given to demonstrate the effectiveness of the proposed results.

scholarly journals Stability and Hopf Bifurcation Analysis of an Epidemic Model by Using the Method of Multiple Scales

2016 ◽  
Vol 2016 ◽  
pp. 1-8 ◽  
Author(s):  
Wanyong Wang ◽  
Lijuan Chen
Keyword(s):  
Periodic Solution ◽  
Hopf Bifurcation ◽  
Time Delay ◽  
Epidemic Model ◽  
Multiple Scales ◽  
Method Of Multiple Scales ◽  
Value Of Time ◽  
Nonlinear Incidence Rate ◽  
The Stability ◽  
Bifurcating Periodic Solution

A delayed epidemic model with nonlinear incidence rate which depends on the ratio of the numbers of susceptible and infectious individuals is considered. By analyzing the corresponding characteristic equations, the effects of time delay on the stability of the equilibria are studied. By choosing time delay as bifurcation parameter, the critical value of time delay at which a Hopf bifurcation occurs is obtained. In order to derive the normal form of the Hopf bifurcation, an extended method of multiple scales is developed and used. Then, the amplitude of bifurcating periodic solution and the conditions which determine the stability of the bifurcating periodic solution are obtained. The validity of analytical results is shown by their consistency with numerical simulations.

A delayed SEIRS epidemic model with impulsive vaccination and nonlinear incidence rate

2014 ◽  
Vol 07 (03) ◽  
pp. 1450032 ◽  
Author(s):  
Jiancheng Zhang ◽  
Jitao Sun
Keyword(s):  
Incidence Rate ◽  
Epidemic Model ◽  
Newborn Infants ◽  
Vaccination Strategy ◽  
Nonlinear Incidence Rate ◽  
Nonlinear Incidence ◽  
Discrete Dynamic System ◽  
Seirs Epidemic Model ◽  
Globally Attractive ◽  
Impulsive Vaccination

In this paper, a delayed SEIRS epidemic model with nonlinear incidence rate and impulsive vaccination is investigated. In vaccination strategy, we perform impulsive vaccination of newborn infants. Using the discrete dynamic system determined by stroboscopic map, we obtain an infection-free periodic solution and establish conditions, on which the solution is globally attractive. We also conclude that the disease is permanent if the parameters of the model satisfy appropriate conditions. Finally, we illustrate the effectiveness of our theorems with numerical simulation. The results obtained in this paper are a good extension of the results obtained in [J. Hou and Z. Teng, Continuous and impulsive vaccination of SEIR epidemic models with saturation incidence rate, Math. Comput. Simulat.79 (2009) 3038–3054] to the corresponding delayed SEIRS epidemic model with nonlinear incidence rate and impulsive vaccination.

A fractional-order epidemic model with time-delay and nonlinear incidence rate

2019 ◽  
Vol 126 ◽  
pp. 97-105 ◽  
Author(s):  
F.A. Rihan ◽  
Q.M. Al-Mdallal ◽  
H.J. AlSakaji ◽  
A. Hashish
Keyword(s):  
Time Delay ◽  
Incidence Rate ◽  
Fractional Order ◽  
Epidemic Model ◽  
Nonlinear Incidence Rate ◽  
Nonlinear Incidence

scholarly journals An SIR Epidemic Model with Time Delay and General Nonlinear Incidence Rate

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Mingming Li ◽  
Xianning Liu
Keyword(s):  
Time Delay ◽  
Incidence Rate ◽  
Epidemic Model ◽  
Transmission Function ◽  
Basic Reproductive Number ◽  
Reproductive Number ◽  
Sir Epidemic Model ◽  
Nonlinear Incidence Rate ◽  
Nonlinear Incidence ◽  
Sir Epidemic

An SIR epidemic model with nonlinear incidence rate and time delay is investigated. The disease transmission function and the rate that infected individuals recovered from the infected compartment are assumed to be governed by general functionsF(S,I)andG(I), respectively. By constructing Lyapunov functionals and using the Lyapunov-LaSalle invariance principle, the global asymptotic stability of the disease-free equilibrium and the endemic equilibrium is obtained. It is shown that the global properties of the system depend on both the properties of these general functions and the basic reproductive numberR0.

scholarly journals Dynamics of a Nonautonomous Stochastic SIS Epidemic Model with Double Epidemic Hypothesis

Complexity ◽  
2017 ◽  
Vol 2017 ◽  
pp. 1-14 ◽  
Author(s):  
Haokun Qi ◽  
Lidan Liu ◽  
Xinzhu Meng
Keyword(s):  
Periodic Solution ◽  
Theoretical Analysis ◽  
Epidemic Model ◽  
Lyapunov Functions ◽  
Sufficient Conditions ◽  
Positive Periodic Solution ◽  
Nonlinear Incidence Rate ◽  
Sis Epidemic Model ◽  
Stochastic Sis Epidemic Model ◽  
Sis Epidemic

We investigate the dynamics of a nonautonomous stochastic SIS epidemic model with nonlinear incidence rate and double epidemic hypothesis. By constructing suitable stochastic Lyapunov functions and using Has’minskii theory, we prove that there exists at least one nontrivial positive periodic solution of the system. Moreover, the sufficient conditions for extinction of the disease are obtained by using the theory of nonautonomous stochastic differential equations. Finally, numerical simulations are utilized to illustrate our theoretical analysis.

scholarly journals On the global stability of a delay epidemic model

1992 ◽  
Vol 34 (1) ◽  
pp. 26-34
Author(s):  
Xiaodong Lin
Keyword(s):  
Periodic Solution ◽  
Asymptotic Behavior ◽  
Time Delay ◽  
Global Stability ◽  
Incidence Rate ◽  
Epidemic Model ◽  
Threshold Value ◽  
Nonlinear Incidence Rate ◽  
Sirs Epidemic Model ◽  
Disease Free

AbstractIn this paper, we study the asymptotic behavior of an SIRS epidemic model with a time delay in the recovered class and a nonlinear incidence rate. A conjecture of Hethcote et al. [5] on the global stability of the disease-free equilibrium is solved. Moreover, we analyse the model when the contact number takes its threshold value. We show that solutions tend to either the disease-free equilibrium or to a unique positive endemic equilibrium, and there is no periodic solution.

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