Discrete Time Si and Sis Epidemic Models With Vertical Transmission

Abstract

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 R 0 , for predicting disease dynamics. R 0 > 1 implies that the disease tends to an endemic equilibrium, while R 0 < 1 implies disease extinction. On the other hand, for the SIS epidemic model with another form force of infection, the basic reproduction number R 0 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.

On the Number of Periodic Inspections During Outbreaks of Discrete-Time Stochastic SIS Epidemic Models

“…In [16], authors introduce probabilities to formulate death, recovery and incidence rates of epidemic diseases on discrete-time SI and SIS epidemic models with vital dynamics. Bistability of discrete-time SI and SIS epidemic models with vertical transmission is the subject matter of [17]. An SIS model with a temporary vaccination program is studied in [18].…”