Global dynamics of a nonautonomous SEIRS epidemic model with vaccination and nonlinear incidence

2021 ◽  
Author(s):  
Long Zhang ◽  
Xiaolin Fan ◽  
Zhidong Teng
Keyword(s):  
Epidemic Model ◽  
Global Dynamics ◽  
Nonlinear Incidence ◽  
Seirs Epidemic Model

scholarly journals Global dynamics of SEIRS epidemic model with non-linear generalized incidences and preventive vaccination

2015 ◽  
Vol 2015 (1) ◽  
Author(s):  
Muhammad Altaf Khan ◽  
Qaisar Badshah ◽  
Saeed Islam ◽  
Ilyas Khan ◽  
Sharidan Shafie ◽  
...  
Keyword(s):  
Epidemic Model ◽  
Global Dynamics ◽  
Seirs Epidemic Model ◽  
Non Linear ◽  
Preventive Vaccination

scholarly journals Hopf Bifurcation Analysis of a New SEIRS Epidemic Model with Nonlinear Incidence Rate and Nonpermanent Immunity

2018 ◽  
Vol 2018 ◽  
pp. 1-13
Author(s):  
M. P. Markakis ◽  
P. S. Douris
Keyword(s):  
Hopf Bifurcation ◽  
Incidence Rate ◽  
Epidemic Model ◽  
Nonlinear Function ◽  
State Variables ◽  
Nonlinear Incidence Rate ◽  
Symbolic Form ◽  
Nonlinear Incidence ◽  
Seirs Epidemic Model ◽  
Critical Regions

A new SEIRS epidemic model with nonlinear incidence rate and nonpermanent immunity is presented in the present paper. The fact that the incidence rate per infective individual is given by a nonlinear function and product of rational powers of two state variables, as well as the introduction of an epidemic-induced death rate, leads to a more realistic modeling of the physical problem itself. A stability analysis is performed and the features of Hopf bifurcation are investigated. Both the corresponding critical regions in the parameter space and their stability characteristics are presented. Furthermore, by using algorithms based on a new symbolic form as regards the restriction of an n-dimensional nonlinear parametric system to the center manifold and the normal forms of the corresponding Hopf bifurcation, as well, the associated bifurcation diagram is derived, and finally various emerging limit cycles are numerically obtained by appropriate implemented methods.

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.

Global dynamics of an epidemic model with relapse and nonlinear incidence

2018 ◽  
Vol 42 (4) ◽  
pp. 1283-1291
Author(s):  
Yuming Chen ◽  
Jianquan Li ◽  
Shaofen Zou
Keyword(s):  
Epidemic Model ◽  
Global Dynamics ◽  
Nonlinear Incidence
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