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

Author:

Adeyemo Kabiru Michael1ORCID,Adam Umar Muhammad2ORCID,Adeniji Adejimi3ORCID,Oshinubi Kayode4ORCID

Affiliation:

1. Department of Mathematics, Hallmark University, Ijebu-Itele 122101, Nigeria

2. Department of Mathematics, Federal University, Dutse 720222, Nigeria

3. Department of Mathematics and Statistics, Tshwane University of Technology, Pretoria 0183, South Africa

4. School of Informatics, Computing and Cyber Systems, Northern Arizona University, Flagstaff, AZ 86011, USA

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 R0≤1 is taken into account. When R0>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 R0<1 but near R0=1 using the Center Manifold Theory. We use the sensitivity analysis method to understand how some parameters influence the R0, 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.

Publisher

MDPI AG

Reference22 articles.

1. Time-delayed modelling of the COVID-19 dynamics with a convex incidence rate;Babasola;Inform. Med. Unlocked,2022

2. Amazigo, U., Noma, M., Bump, J., Benton, B., Liese, B., Yaméogo, L., Zouré, H., and Seketeli, A. (2006). Disease and Mortality in Sub-Saharan Africa, The International Bank for Reconstruction and Development/The World Bank. [2nd ed.].

3. Competitive dynamics in a model for Onchocerciasis with cross-immunity;Mopecha;Can. Appl. Math. Q.,2003

4. World Health Organization (2012). African Programme for Onchocerciasis Control: Meeting of national onchocerciasis task forces, September 2012. Wkly. Epidemiol. Rec. Relev. Épid. Hebd., 87, 494–502.

5. Infectious disease and species coexistence: A model of Lotka-Volterra form;Holt;Am. Nat.,1985

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