Pulse Vaccination Strategy in an SIVS Epidemic Model with General Nonlinear Incidence Rate

2016 ◽  
Vol 1 (2) ◽  
Author(s):  
Dan Yu ◽  
◽  
Shujing Gao ◽  
Youquan Luo ◽  
Feiping Xie ◽  
...  
Keyword(s):  
Incidence Rate ◽  
Epidemic Model ◽  
Vaccination Strategy ◽  
Nonlinear Incidence Rate ◽  
Nonlinear Incidence ◽  
Pulse Vaccination

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.

Stability Properties of Pulse Vaccination Strategy in the SIVS Epidemic Models with Nonlinear Incidence Rate

2012 ◽  
Vol 198-199 ◽  
pp. 819-823
Author(s):  
Yan Song
Keyword(s):  
Incidence Rate ◽  
Vaccination Strategy ◽  
Epidemic Models ◽  
Asymptotically Stable ◽  
Nonlinear Incidence Rate ◽  
Globally Asymptotically Stable ◽  
Nonlinear Incidence ◽  
Stability Properties ◽  
Pulse Vaccination ◽  
The Stability

In this paper, we discuss the SIVS epidemic models with vertical transmission and nonlinear incidence rate. We study the stability properties of pulse vaccination strategy in the models and obtain the sufficient condition for which the epidemic elimination solution is globally asymptotically stable.

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.

Sign in / Sign up

Export Citation Format

Share Document