Stability of a continuous time model

A qualitative analysis of an SIV (susceptible-infected-vaccinated) model of the spread of gonorrhea in a homosexually active population is performed. A basic reproduction number ℝo is identified and a threshold nature of the disease is established; it is shown that if ℝo < 1, the disease free equilibrium is globally asymptotically stable implying the disappearance of the disease in the population; if ℝo > 1 then it is shown that the endemic equilibrium is globally asymptotically stable implying the invasion of the population by the disease. These results are established by using the theory of the asymptotically autonomous differential equations. Copyright © 2011 Dynamic Publishers, Inc.