Impulsive vaccination of SEIR epidemic model with time delay and nonlinear incidence rate

2008 ◽  
Vol 79 (3) ◽  
pp. 500-510 ◽  
Author(s):  
Zhong Zhao ◽  
Lansun Chen ◽  
Xinyu Song
Keyword(s):  
Time Delay ◽  
Incidence Rate ◽  
Epidemic Model ◽  
Nonlinear Incidence Rate ◽  
Nonlinear Incidence ◽  
Impulsive Vaccination

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.

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.

Dynamical analysis of a reaction–diffusion SEI epidemic model with nonlinear incidence rate

2021 ◽  
pp. 2150041
Author(s):  
Jianpeng Wang ◽  
Binxiang Dai
Keyword(s):  
Steady State ◽  
Incidence Rate ◽  
Epidemic Model ◽  
Reaction Diffusion ◽  
Dynamical Analysis ◽  
Asymptotically Stable ◽  
Nonlinear Incidence Rate ◽  
Globally Asymptotically Stable ◽  
Nonlinear Incidence ◽  
Positive Steady State

In this paper, a reaction–diffusion SEI epidemic model with nonlinear incidence rate is proposed. The well-posedness of solutions is studied, including the existence of positive and unique classical solution and the existence and the ultimate boundedness of global solutions. The basic reproduction numbers are given in both heterogeneous and homogeneous environments. For spatially heterogeneous environment, by the comparison principle of the diffusion system, the infection-free steady state is proved to be globally asymptotically stable if [Formula: see text] if [Formula: see text], the system will be persistent and admit at least one positive steady state. For spatially homogenous environment, by constructing a Lyapunov function, the infection-free steady state is proved to be globally asymptotically stable if [Formula: see text] and then the unique positive steady state is achieved and is proved to be globally asymptotically stable if [Formula: see text]. Finally, two examples are given via numerical simulations, and then some control strategies are also presented by the sensitive analysis.

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