Mathematical modeling of COVID-19 with a constant spatial diffusion term in Ghana

Document Type : Research Paper

Authors

1 Department of Mathematics, College of Science, Kwame Nkrumah University of Science and Technology, Ghana.

2 Kwame Nkrumah University of Science and Technology Senior High School, Ghana.

Abstract

The purpose of this study is to develop a mathematical model that incorporates a diffusion term in one dimension in the dynamics of coronavirus disease-19 (COVID-19) in Ghana. A reaction-diffusion model is derived by applying the law of conservation of matter and Fick's law, which are fundamental theorems in fluid dynamics. Since COVID-19 is declared to be a pandemic, most African countries are affected by the negative impacts of the disease. However, controlling the spread becomes a challenge for many developing countries like Ghana. A lot of studies about the dynamics of the infection do not consider the fact that since the disease is pandemic, its model should be spatially dependent, therefore failing to incorporate the diffusion aspect. In this study, the local and global stability analyses are carried out to determine the qualitative solutions to the SEIQRF model. Significant findings are made from these analyses as well as the numerical simulations and results. The basic reproduction number ($R_o$) calculated at the disease-free fixed point is obtained to be $R_o\approx2.5$, implying that, an infectious individual is likely to transmit the coronavirus to about three susceptible persons. A Lyapunov functional constructed at the endemic fixed point also explains that the system is globally asymptotically stable, meaning that COVID-19 will be under control in Ghana for a long period of time. 

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Computational Methods for Differential Equations
Volume 13, Issue 3
July 2025
Pages 870-884

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History

  • Receive Date: 30 October 2023
  • Revise Date: 30 July 2024
  • Accept Date: 11 August 2024

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