Some discrete SI and SIS epidemic models

The probability is introduced to formulate the death of individuals, the recovery of the infected individuals and incidence of epidemic disease. Based on the assumption that the number of individuals in a population is a constant, discrete-time SI and SIS epidemic models with vital dynamics are established respectively corresponding to the case that the infectives can recover from the disease or not. For these two models, the results obtained in this paper show that there is the same dynamical behavior as their corresponding continuous ones, and the threshold determining its dynamical behavior is found. Below the threshold the epidemic disease dies out eventually, above the threshold the epidemic disease becomes an endemic eventually, and the number of the infectives approaches a positive constant.