Mathematical modelling of dengue fever transmission dynamics in Kenya

Brian  Nyanaro; George  Kimathi; Mary  Wainaina

doi:10.59400/jam1807

Mathematical modelling of dengue fever transmission dynamics in Kenya

Brian Nyanaro Department of Mathematics and Actuarial Science, Catholic University of Eastern Africa, Nairobi Box 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 Box 62157-00200, Kenya

Article ID: 1807

47 Views, 21 PDF Downloads

DOI: https://doi.org/10.59400/jam1807

Keywords: basic reproductive number; dengue fever; equilibrium points; mathematical modelling; numerical simulations

Abstract

Dengue fever is one of the diseases emerging in Kenya due to effects of climate change and urbanization. The disease is caused by a family of four flavivirus serotypes DENV 1 to DENV4. A deterministic compartmental model for the dengue fever spread dynamics was developed and utilized to examine dengue fever spread dynamics in Kenya. The model was established to be well-stated mathematically and epidemiologically well-posed through positivity and boundedness analysis. The dengue-free equilibrium state was determined as part of the solution to the system of differential equations defining the spread dynamics. The basic reproduction number was determined through the next-generation matrix and used to confirm the stability of the steady state determined before. The study found that when the basic reproduction number was greater than one, the dengue endemic state dominated the solution of the spread dynamics, while when the basic reproduction number was less than one, the dengue free state dominated the solution, implying the disease died down progressively. Sensitivity analysis of the basic reproduction number was carried out to determine the candidate parameters for an optimal control solution. The study found that the infection rate of susceptible mosquitoes, the survival rate of pre-adult mosquitoes, the natural death rate of mosquitoes, the rate at which mosquito survived the extrinsic incubation stage, and the egg-laying of mosquitoes were the most sensitive parameters of the model.

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Published

2024-12-17

How to Cite

Nyanaro, B., Kimathi, G., & Wainaina, M. (2024). Mathematical modelling of dengue fever transmission dynamics in Kenya. Journal of AppliedMath, 2(5), 1807. https://doi.org/10.59400/jam1807

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