Optimal control of dengue fever transmission dynamics in Kenya

Brian  Nyanaro; George Kimathi; Mary Wainaina

doi:10.59400/jam2353

Optimal control of dengue fever transmission dynamics in Kenya

Brian Nyanaro Department of Mathematics and Actuarial Science, Catholic University of Eastern Africa, Nairobi 62157-00200, Kenya
George Kimathi School of Computing and Information Technology, University of Kigali, Kigali 101, Rwanda
Mary Wainaina Department of Mathematics and Actuarial Science, Catholic University of Eastern Africa, Nairobi 62157-00200, Kenya

Article ID: 2353

Keywords: adjoints; basic reproductive number; dengue fever; mathematical modelling; numerical simulations; optimal control; Pontrayagin’s maximum principle; the Hamiltonian

Abstract

The emergence of dengue fever in Kenya has been witnessed in the recent past, leading to public health alerts and disruption of economic activities. The outbreaks have mainly been restricted to the Northeastern and Coastal counties of the country. As such, this paper has focused on an epidemiological model that incorporates an optimal control model of the spread dynamics of dengue fever in Kenya. The objective of the study is to develop an optimal control solution for the spread dynamics of dengue fever in Kenya. This study introduced three time-dependent control variables, which were divided into long-term and short-term control measures. The short-term control measures include prophylactics (treatment) and the use of physical barriers (nets), while the long-term control measure is the treatment of Aedes aegypti mosquitoes with Wolbachia bacteria. The basic reproduction number with the control variables was determined. The set of adjoint points of the control systems was obtained together with the optimal control set. The numerical solutions to the control problem were obtained by use of the forward-backward sweep method and the Runge-Kutta order four method. The impact of utilizing various strategies that employed the combination of the three control measures in different combinations was examined. The control profile of the particular control measures used was also investigated. It was determined that the short-term control measures had more impact on the control of the spread dynamics of dengue fever when compared to the long-term control measure. As such, it was determined that a strategy that incorporates both the long-term and short-term control measures should be utilized for optimum control of dengue fever spread dynamics in Kenya.

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Published

2025-03-11

How to Cite

Nyanaro, B., Kimathi, G., & Wainaina, M. (2025). Optimal control of dengue fever transmission dynamics in Kenya. Journal of AppliedMath, 3(2), 2353. https://doi.org/10.59400/jam2353

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