Mathematical Modeling of Two Interacting Populations’ Dynamics of Onchocerciasis Disease Spread with Nonlinear Incidence Functions

Kabiru Michael Adeyemo, Umar Muhammad Adam, Adejimi Adeniji and Kayode Oshinubi ()
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Kabiru Michael Adeyemo: Department of Mathematics, Hallmark University, Ijebu-Itele 122101, Nigeria
Umar Muhammad Adam: Department of Mathematics, Federal University, Dutse 720222, Nigeria
Adejimi Adeniji: Department of Mathematics and Statistics, Tshwane University of Technology, Pretoria 0183, South Africa
Kayode Oshinubi: School of Informatics, Computing and Cyber Systems, Northern Arizona University, Flagstaff, AZ 86011, USA

Mathematics, 2024, vol. 12, issue 2, 1-22

Abstract: The transmission dynamics of onchocerciasis in two interacting populations are examined using a deterministic compartmental model with nonlinear incidence functions. The model undergoes qualitative analysis to examine how it behaves near disease-free equilibrium (DFE) and endemic equilibrium. Using the Lyapunov function, it is demonstrated that the DFE is globally stable when the threshold parameter R 0 ≤ 1 is taken into account. When R 0 > 1 , it suffices to show globally how asymptotically stable the endemic equilibrium is and its existence. We conduct the bifurcation analysis by looking at the possibility of the model’s equilibria coexisting at R 0 < 1 but near R 0 = 1 using the Center Manifold Theory. We use the sensitivity analysis method to understand how some parameters influence the R 0 , hence the transmission and mitigation of the disease dynamics. Furthermore, we simulate the model developed numerically to understand the population dynamics. The outcome presented in this article offers valuable understanding of the transmission dynamics of onchocerciasis, specifically in the context of two populations that interact with each other, considering the presence of nonlinear incidence.

Keywords: population dynamics; bifurcation analysis; sensitivity analysis; onchocerciasis epidemic model; nonlinear dynamics (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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