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

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 R01 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.

Keywords

• population dynamics
• bifurcation analysis
• sensitivity analysis
• onchocerciasis epidemic model
• nonlinear dynamics