An SIS epidemic model with variable population size and a delay

1995 ◽  
Vol 34 (2) ◽  
pp. 177-194 ◽  
Author(s):  
Herbert W. Hethcote ◽  
P. van den Driessche
Keyword(s):  
Population Size ◽  
Epidemic Model ◽  
Sis Epidemic Model ◽  
Variable Population ◽  
Sis Epidemic ◽  
Variable Population Size

A KICKED EPIDEMIC SIRS MODEL

2012 ◽  
Vol 22 (10) ◽  
pp. 1250251
Author(s):  
F. PALADINI ◽  
I. RENNA ◽  
L. RENNA
Keyword(s):  
Infectious Diseases ◽  
Numerical Simulations ◽  
Population Size ◽  
Discrete Time ◽  
Epidemic Model ◽  
Seasonal Variability ◽  
Sirs Model ◽  
Variable Population ◽  
Variable Population Size

A discrete-time deterministic epidemic model is proposed with the aim of reproducing the behavior observed in the incidence of real infectious diseases, such as oscillations and irregularities. For this purpose, we introduce, in a naïve discrete-time SIRS model, seasonal variability (i) in the loss of immunity and (ii) in the infection probability, modeled by sequences of kicks. Effects of a variable population size (assumed as logistic) are also analyzed. Restrictive assumptions are made on the parameters of the models, in order to guarantee that the transitions are determined by true probabilities, so that comparisons with stochastic discrete-time previsions can be also provided. Numerical simulations show that the characteristics of real infectious diseases can be adequately modeled.

Disease extinction and persistence in a discrete-time sis epidemic model with vaccination and varying population size

Filomat ◽  
2017 ◽  
Vol 31 (15) ◽  
pp. 4735-4747 ◽  
Author(s):  
Rahman Farnoosh ◽  
Mahmood Parsamanesh
Keyword(s):  
Population Size ◽  
Discrete Time ◽  
Epidemic Model ◽  
Jacobian Matrix ◽  
Sufficient Conditions ◽  
Period Doubling ◽  
System Of Difference Equations ◽  
Sis Epidemic Model ◽  
Necessary And Sufficient ◽  
Sis Epidemic

A discrete-time SIS epidemic model with vaccination is introduced and formulated by a system of difference equations. Some necessary and sufficient conditions for asymptotic stability of the equilibria are obtained. Furthermore, a sufficient condition is also presented. Next, bifurcations of the model including transcritical bifurcation, period-doubling bifurcation, and the Neimark-Sacker bifurcation are considered. In addition, these issues will be studied for the corresponding model with constant population size. Dynamics of the model are also studied and compared in detail with those found theoretically by using bifurcation diagrams, analysis of eigenvalues of the Jacobian matrix, Lyapunov exponents and solutions of the models in some examples.

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