Bifurcations and chaos in discrete-time gonorrhea model

Abstract

A deterministic epidemic model for the spread of gonorrhea is investigated in discrete-time by taking into account the interval between successive clinical cases. It is shown that the discrete-time dynamical system exhibits far more complex dynamics than its continuous analogues. Stability analysis is obtained in order to investigate the local stability properties of the fixed points; it is verified that there are phenomena of Fold and Flip bifurcations. Numerical simulation tools are used in order to illustrate the stability analysis results and find some new qualitative dynamics. We come across the phenomenon of “intermittency route to chaos”. The density of infected individuals goes through quasi-periodicity and a strange attractor appears in the system. Chaos control is obtained in order to see how the male latex condom use during sexual intercourse affects the incidence of gonorrhea. It is shown that male latex condom use stabilizes the chaotic vibrations of the system to a point where the number of infected individuals remains stable and is significantly small or zero, leading to the control of disease. © 2014 ISAST