TY - JOUR
T1 - Mathematics of a sex-structured model for syphilis transmission dynamics
AU - Gumel, Abba
AU - M.-S. Lubuma, Jean
AU - Sharomi, Oluwaseun
AU - Terefe, Yibeltal Adane
N1 - Funding Information:
Two of the authors (Y.A.T. and J.M.S.L.) are grateful to the DST/NRF SARChI Chair in Mathematical Models and Methods in Bioengineering and Biosciences for generous financial support. The authors are grateful to the anonymous reviewers for their constructive comments, which have improved the manuscript.
Publisher Copyright:
Copyright © 2018 John Wiley & Sons, Ltd.
PY - 2018/12
Y1 - 2018/12
N2 - 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.
AB - 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.
KW - bifurcation
KW - reinfection
KW - reproduction number
KW - stability
KW - syphilis
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U2 - 10.1002/mma.4734
DO - 10.1002/mma.4734
M3 - Article
AN - SCOPUS:85044411262
SN - 0170-4214
VL - 41
SP - 8488
EP - 8513
JO - Mathematical Methods in the Applied Sciences
JF - Mathematical Methods in the Applied Sciences
IS - 18
ER -