A time-varying SIS epidemic model with incidence rate depending on the susceptible and infective populations with eventual impulsive effects

2013 ◽  
Vol 219 (10) ◽  
pp. 5516-5536 ◽  
Author(s):  
M. De la Sen ◽  
A. Ibeas ◽  
S. Alonso-Quesada
Keyword(s):  
Incidence Rate ◽  
Epidemic Model ◽  
Impulsive Effects ◽  
Time Varying ◽  
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 Positive Periodic Solutions for an Generalized SIS Epidemic Model with Time-Varying Coefficients and Delays

2018 ◽  
Vol 2018 ◽  
pp. 1-5
Author(s):  
Zhiwen Long
Keyword(s):  
Periodic Solutions ◽  
Epidemic Model ◽  
Time Varying ◽  
Positive Periodic Solutions ◽  
Varying Coefficients ◽  
Sis Epidemic Model ◽  
Lyapunov Function Method ◽  
Time Varying Coefficients ◽  
Theoretical Results ◽  
Sis Epidemic

This paper mainly explores a generalized SIS epidemic model with time-varying coefficients and delays. By employing Lyapunov function method and differential inequality approach, a sufficient criterion to guarantee the existence and exponential stability of positive periodic solutions for the addressed model is obtained, which complements the earlier publications. Particularly, an example and its numerical simulations are given to demonstrate our theoretical results.

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