Analysis of an SIS Epidemic Model with Disease-Induced Mortality

The probability is introduced to establish the discrete-time SIS epidemic model which considers disease-induced mortality and has constant recruitment. And the threshold determining its dynamical behavior is found. Below the threshold, the model only has the disease-free equilibrium which is globally asymptotically stable. Above the threshold, the model is uniformly persistent and has a unique endemic equilibrium which is supposed to be globally asymptotically stable.