Dynamics of Continuous and Discrete Time Siv Models of Gonorrhea Transmission

A continuous-time SIV (susceptible-infected-vaccinated) model of the transmission of Gonorrhea among homosexuals is analyzed. A basic reproduction number Ro is identified and it is shown that the disease-free equilibrium is globally asymptotically stable when Ro ≤ 1. It is also shown that this equilibrium is unstable when Ro > 1 and there exists a globally asymptotically stable endemic equilibrium in this case. These results are obtained by using the theory of asymptotically autonomous dynamical systems to reduce progressively the dimension of the systems. A nonstandard discretization method is used to formulate a discrete time model and it is shown that this discrete-time model preserves some important dynamical characteristics of the continuous time model including the basic reproduction number. The results of the discrete-time model and the basic reproduction number do not depend on the discretization step size and are exactly the same as those of the continuous time model.