## Abstract

A continuous-time SIV (susceptible-infected-vaccinated) model of the trans- mission of Gonorrhea among homosexuals is analyzed. A basic reproduction number R _{o} is identified and it is shown that the disease-free equilibrium is globally asymptotically stable when R _{o}≤ 1: It is also shown that this equilibrium is unstable when R _{o} > 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.

Original language | English |
---|---|

Pages (from-to) | 351-375 |

Number of pages | 25 |

Journal | Dynamics of Continuous, Discrete and Impulsive Systems. Series B: Applications and Algorithms |

Volume | 19 |

Issue number | 3 |

Publication status | Published - 2012 |

## Keywords

- Asymptot-ically Autonomous
- Basic Reproduction Number
- Disease-Free Equilibrium
- Endemic E-quilibrium
- Global Stability
- Gonorrhea Transmission
- Non-Standard Discretization Method
- Threshold Behavior