Dynamics of continuous and discrete time siv models of Gonorrhea transmission

Kui Chiu Issic LEUNG, K. GOPALSAMY

Research output: Contribution to journalArticles

1 Citation (Scopus)

Abstract

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.
Original languageEnglish
Pages (from-to)351-375
JournalDynamics of Continuous, Discrete and Impulsive Systems Series B: Applications and Algorithms
Volume19
Issue number3
Publication statusPublished - 2012

Citation

Leung, 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.

Keywords

  • Gonorrhea transmission
  • Non-standard discretization method
  • Asymptotically autonomous
  • Basic reproduction number
  • Disease-free equilibrium
  • Endemic equilibrium
  • Global stability
  • Threshold behavior

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