Mathematics of a sex-structured model for syphilis transmission dynamics

Abba Gumel, Jean M.-S. Lubuma, Oluwaseun Sharomi, Yibeltal Adane Terefe

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

Syphilis, a major sexually transmitted disease, continues to pose major public health burden in both underdeveloped and developed nations of the world. This study presents a new 2-group sex-structured model for assessing the community-level impact of treatment and condom use on the transmission dynamics and control of syphilis. Rigorous analysis of the model shows that it undergoes the phenomenon of backward bifurcation. In the absence of this phenomenon (which is shown to arise because of the reinfection of recovered individuals), the disease-free equilibrium of the model is shown to be globally asymptotically stable when the associated reproduction number is less than unity. Furthermore, the model can have multiple endemic equilibria when the reproduction threshold exceeds unity. Numerical simulations of the model, using data relevant to the transmission dynamics of the disease in Nigeria, show that, with the assumed 80% condom efficacy, the disease will continue to persist (ie, remain endemic) in the population regardless of the level of compliance in condom usage by men. Furthermore, detailed optimal control analysis (using Pontraygin's maximum principle) reveals that, for situations where the cost of implementing the controls (treatment and condom-use) considered in this study is low, channelling resources to a treatment-only strategy is more effective than channelling them to a condom-use only strategy. Furthermore, as expected, the combined condom-treatment strategy provides a higher population-level impact than the treatment-only strategy or the condom-use only strategy. When the cost of implementing the controls is high, the 3 strategies are essentially equally as ineffective.

Original languageEnglish (US)
JournalMathematical Methods in the Applied Sciences
DOIs
StateAccepted/In press - Jan 1 2018

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Maximum principle
Model
Backward Bifurcation
Multiple Equilibria
Reproduction number
Public health
Endemic Equilibrium
Globally Asymptotically Stable
Public Health
Costs
Maximum Principle
Compliance
Data Model
Strategy
Efficacy
Exceed
Optimal Control
Computer simulation
Numerical Simulation

Keywords

  • Bifurcation
  • Reinfection
  • Reproduction number
  • Stability
  • Syphilis

ASJC Scopus subject areas

  • Mathematics(all)
  • Engineering(all)

Cite this

Mathematics of a sex-structured model for syphilis transmission dynamics. / Gumel, Abba; M.-S. Lubuma, Jean; Sharomi, Oluwaseun; Terefe, Yibeltal Adane.

In: Mathematical Methods in the Applied Sciences, 01.01.2018.

Research output: Contribution to journalArticle

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