Mathematical Modeling and Numerical Simulation of Drug Consumption Dynamics in Burkina Faso

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DOI: https://doi.org/10.28924/2291-8639-23-2025-12
Published: Jan 14, 2025
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Pegdwindé Ousséni Fabrice Ouédraogo, Yamba Malick Siemde, Wenddabo Olivier Sawadogo, Adama Kiemtoré, Mathematical Modeling and Numerical Simulation of Drug Consumption Dynamics in Burkina Faso, Int. J. Anal. Appl., 23 (2025), 12.

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Pegdwindé Ousséni Fabrice Ouédraogo, Yamba Malick Siemde, Wenddabo Olivier Sawadogo, Adama Kiemtoré

Abstract

In this paper a mathematical model of drug consumption dynamics is proposed and analyzed. The model is based on the principle of the epidemiological model and takes into account the biological and environmental factors of exposed individuals, treatment and sensitization. The Jacobian determinant method is used to determine the basic reproduction function R0 of the model. The drug-free equilibrium points and the endemic equilibrium of the model were then identified, and their stabilities were analyzed based on the value of R0. A sensitivity analysis was performed to assess which parameters have the greatest influence on the dynamics of drug consumption. The numerical simulation was carried out using data from the Burkinabe population in 2020, aged between 11 and 65 years. The numerical results show that sensitization and treatment do not have much effect if the individual evolves in a favorable environment.

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