Stability and Hopf bifurcation analysis of an SIS epidemic model with latency and nonlinear incidence rate

2019 ◽  
Author(s):  
Anthony M. Pasion ◽  
Juancho A. Collera
Keyword(s):  
Hopf Bifurcation ◽  
Incidence Rate ◽  
Bifurcation Analysis ◽  
Epidemic Model ◽  
Nonlinear Incidence Rate ◽  
Nonlinear Incidence ◽  
Sis Epidemic Model ◽  
Sis Epidemic

A SIS Epidemic Model with Eventual Impulsive Effects

2013 ◽  
Vol 393 ◽  
pp. 666-674
Author(s):  
Manuel de La Sen ◽  
A. Ibeas ◽  
S. Alonso-Quesada
Keyword(s):  
Incidence Rate ◽  
Epidemic Model ◽  
Total Population ◽  
Disease Model ◽  
Impulsive Effects ◽  
Time Varying ◽  
Nonlinear Incidence Rate ◽  
Nonlinear Incidence ◽  
Sis Epidemic Model ◽  
Sis Epidemic

This paper studies a time-varyingSIS(i.e.containing susceptible and infected populations) propagation disease model exhibiting a nonlinear incidence rate and impulsive eventual culling of both populations so that the individuals recover with no immunity to the disease. The nonlinear incidence rate consists of two time-varying additive terms proportional to the susceptible and infected populations normalized to the total population.

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.

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