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. Copyright © 2012 Watam Press.
|Journal||Dynamics of Continuous, Discrete and Impulsive Systems Series B: Applications and Algorithms|
|Publication status||Published - 2012|
CitationLeung, I. K. C., & Gopalsamy, K. (2012). Dynamics of continuous and discrete time siv models of Gonorrhea transmission. Dynamics of Continuous, Discrete and Impulsive Systems Series B: Applications and Algorithms, 19(3), 351-375.
- Gonorrhea transmission
- Non-standard discretization method
- Asymptotically autonomous
- Basic reproduction number
- Disease-free equilibrium
- Endemic equilibrium
- Global stability
- Threshold behavior