Modelling the dynamics of syphilis infection with personal protection and treatment as optimal control strategies

Elvis Kobina  Donkor; Bismark  Ansu; Shaibu  Osman; Dominic  Otoo; Winnie Mokeira  Onsongo; Ernest Yeboah  Boateng

doi:10.59400/jam.v2i3.179

Modelling the dynamics of syphilis infection with personal protection and treatment as optimal control strategies

Elvis Kobina Donkor Department of Mathematics and Statistics, University of Energy and Natural Resources, Sunyani P. O. Box 214, Ghana
Bismark Ansu Department of Mathematics and ICT, St. Ambrose College of Education, Dormaa-Akwamu P. O. Box 25, Ghana
Shaibu Osman Department of Basic Sciences, School of Basic and Biomedical Sciences, University of Health and Allied Sciences, Ho PO Box 31, Ghana
Dominic Otoo Department of Mathematics and Statistics, University of Energy and Natural Resources, Sunyani P. O. Box 214, Ghana
Winnie Mokeira Onsongo Department of Statistics and Actuarial Science, University of Ghana, Legon P. O. Box LG 25, Ghana
Ernest Yeboah Boateng Department of Basic Sciences, School of Basic and Biomedical Sciences, University of Health and Allied Sciences, Ho PO Box 31, Ghana

Article ID: 179

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DOI: https://doi.org/10.59400/jam.v2i3.179

Keywords: Syphilis infection; non-linear model; equilibria; Pontryagin’s Maximum Principle; optimal control

Abstract

Syphilis is a sexually transmitted infection which when left untreated would lead to major health problems. Syphilis can easily be contracted by direct contact with Syphilis sore during vaginal, anal, or oral sex. Syphilis can also be passed on from an infected mother to her unborn child. In this paper, a nonlinear deterministic model of Syphilis disease was constructed to determine the dynamics of Syphilis infections. The study deduced model’s equilibria and analyzed the local and global stability of these equilibria. The model was extended to optimal control problem by adding time-dependent controls that helped characterize a range of possible controls that minimized the disease. The control system was solved qualitatively and numerically to evaluate the effectiveness of the considered controls using Pontryagin’s Maximum Principle. The analysis indicated that strategies B and C are considered most effective as they substantially minimized the exposed, asymptomatic and symptomatic infectious. We recommend that stakeholders should consider strategy B and C in their effort to miti-gate the disease from the population as they all have the same effect of substantially minimizing the exposed, symptomatic and asymptomatic populations.

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Published

2024-06-24

How to Cite

Donkor, E. K., Ansu, B., Osman, S., Otoo, D., Onsongo, W. M., & Boateng, E. Y. (2024). Modelling the dynamics of syphilis infection with personal protection and treatment as optimal control strategies. Journal of AppliedMath, 2(3), 179. https://doi.org/10.59400/jam.v2i3.179

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