Epidemiology is the study of the spread of infectious diseases with the objective totrace factors that contribute to their dynamics and stabilities. Formerly and recently models, which have the population subclasses (i) the susceptibles (S), (ii) the infectives (I)and (iii) the removals (R), have been studied by a number of authors (see for exampleBailey [2], Tornatore [12], Beretta and Takeuchi [3], Zhang and Teng [13]). The basicand important research subjects for recent studies are the existence of the threshold valueswhich distinguish whether the disease dies out, the stability of the disease-free and the endemic equilibria, permanence and extinction. Most of these works deal with local stability