Some discrete-time SI, SIR, and SIS epidemic models

1994 ◽  
Vol 124 (1) ◽  
pp. 83-105 ◽  
Author(s):  
Linda J.S. Allen
Keyword(s):  
Discrete Time ◽  
Epidemic Models ◽  
Sis Epidemic

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 Persistence-time estimation for some stochastic SIS epidemic models

2015 ◽  
Vol 20 (9) ◽  
pp. 2933-2947 ◽  
Author(s):  
Francisco de la Hoz ◽  
Anna Doubova ◽  
Fernando Vadillo
Keyword(s):  
Time Estimation ◽  
Epidemic Models ◽  
Persistence Time ◽  
Sis Epidemic

scholarly journals Demographic population cycles and ℛ0in discrete-time epidemic models

2018 ◽  
Vol 13 (sup1) ◽  
pp. 179-200
Author(s):  
P. van den Driessche ◽  
Abdul-Aziz Yakubu
Keyword(s):  
Discrete Time ◽  
Population Cycles ◽  
Epidemic Models
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