Mathematical modelling of transmission dynamics of Dengue Fever in the presence of infective immigrants

Elvis Kobina  Donkoh; Dominic  Otoo; Shaibu  Osman; Maxwell  Baafi; Martin  Anokye; Ernest Yeboah  Boateng

doi:10.59400/jam.v2i3.160

Mathematical modelling of transmission dynamics of Dengue Fever in the presence of infective immigrants

Elvis Kobina Donkoh Department of Mathematics and Statistics, University of Energy and Natural Resources, Sunyani, P. O. Box 214, Ghana
Dominic Otoo Department of Mathematics and Statistics, University of Energy and Natural Resources, Sunyani, P. O. Box 214, Ghana
Shaibu Osman Department of Basic Sciences, School of Basic and Biomedical Sciences, University of Health and Allied Sciences, Ho, PMB 31, Ghana
Maxwell Baafi Department of Mathematics and Statistics, University of Energy and Natural Resources, Sunyani, P. O. Box 214, Ghana
Martin Anokye Department of Mathematics, University of Cape Coast, Cape Coast, P. O. Box 5007, Ghana
Ernest Yeboah Boateng Department of Basic Sciences, School of Basic and Biomedical Sciences, University of Health and Allied Sciences, Ho, PMB 31, Ghana

Ariticle ID: 160

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DOI: https://doi.org/10.59400/jam.v2i3.160

Keywords: Dengue Model; endemic equilibrium; infectious immigrants; reproduction number

Abstract

Dengue fever is one of the neglected tropical diseases around the globe and its ravaging effect over the period has been enormous in the affected areas. Globalisation, immigration and urbanization and poor urban planning have become the contributory factors in the spread of infectious diseases. In this paper, a model describing the dynamics of dengue fever incorporated with infection immigrants is formulated and analysed using ordinary differential equations with a constant immigration recruitment rate. The model was qualitatively and quantitatively analysed for its local stability, basic reproductive number and sensitivity of the model parameters values to the basic reproductive number to understand the impact of the parameters on the disease spread. In the analysis, it was found that in the presence of infectious immigrants, there cannot be a disease free state demonstrated by ∅ ≥ 0 where the model demonstrates a unique endemic equilibrium state if the fraction of infectious immigrants ∅ is positive. The unique endemic equilibrium for which there is a fraction of infectious immigrants is globally asymptotically stable. Numerical simulation was performed and the results displayed graphically and discussed. It was revealed that immigration of infected immigrants contributes significantly in the spread of dengue fever and that it can be controlled by preventing the influx of infected immigrants and reducing the mosquitoes and human contact rate.

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Published

2024-05-08

How to Cite

Donkoh, E. K., Otoo, D., Osman, S., Baafi, M., Anokye, M., & Boateng, E. Y. (2024). Mathematical modelling of transmission dynamics of Dengue Fever in the presence of infective immigrants. Journal of AppliedMath, 2(3), 160. https://doi.org/10.59400/jam.v2i3.160

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