Allee effects in a discrete-time SIS epidemic model with infected newborns

2007 ◽  
Vol 13 (4) ◽  
pp. 341-356 ◽  
Author(s):  
Abdul-Aziz Yakubu
Keyword(s):  
Discrete Time ◽  
Epidemic Model ◽  
Allee Effects ◽  
Sis Epidemic Model ◽  
Sis Epidemic

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.

DISCRETE TIME SI AND SIS EPIDEMIC MODELS WITH VERTICAL TRANSMISSION

2009 ◽  
Vol 17 (02) ◽  
pp. 201-212 ◽  
Author(s):  
JUPING ZHANG ◽  
ZHEN JIN
Keyword(s):  
Vertical Transmission ◽  
Discrete Time ◽  
Epidemic Model ◽  
Epidemic Models ◽  
Basic Reproductive Number ◽  
Reproductive Number ◽  
Epidemic Threshold ◽  
Sis Epidemic Model ◽  
Wide Range ◽  
Sis Epidemic

Discrete time SI and SIS epidemic models with vertical transmission are presented in this paper. With regard to the SI model with constant or variable population size, we introduce an epidemic threshold parameter, the basic reproductive number R0, for predicting disease dynamics. R0 > 1 implies that the disease tends to an endemic equilibrium, while R0 < 1 implies disease extinction. On the other hand, for the SIS epidemic model with another form force of infection, the basic reproduction number R0 determines the persistence or extinction of the disease. In the same time, we also explore the relationship between the demographic equation and the epidemic process. In particular, we show that the epidemic model can exhibit bistability (alternative stable equilibria) over a wide range of parameter values.

scholarly journals Endemic Behaviour of SIS Epidemics with General Infectious Period Distributions

2014 ◽  
Vol 46 (01) ◽  
pp. 241-255 ◽  
Author(s):  
Peter Neal
Keyword(s):  
Epidemic Model ◽  
Branching Process ◽  
Endemic Equilibrium ◽  
Infectious Period ◽  
Sis Epidemic Model ◽  
Branching Process With Immigration ◽  
Sis Epidemic ◽  
Sis Epidemics ◽  
Surprising Observation

We study the endemic behaviour of a homogeneously mixing SIS epidemic in a population of size N with a general infectious period, Q, by introducing a novel subcritical branching process with immigration approximation. This provides a simple but useful approximation of the quasistationary distribution of the SIS epidemic for finite N and the asymptotic Gaussian limit for the endemic equilibrium as N → ∞. A surprising observation is that the quasistationary distribution of the SIS epidemic model depends on Q only through

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