Transmission dynamics of onchocerciasis with two classes of infection and saturated treatment function

Abstract

A mathematical model describing the epidemic interactions between humans and blackflies in the transmission of onchocerciasis is considered. In this model, the onchocerciasis infected human individuals are divided into two classes of infected humans with high and low microfilarial output incorporating saturated treatment function, which caters for high saturation of onchocerciasis disease. We analyze the model feasible region and obtain the basic reproduction number [Formula: see text] using the next generation matrix method. Also, we obtain the onchocerciasis-free and onchocerciasis endemic equilibrium solutions and show that if [Formula: see text] is less than unity, the onchocerciasis-free equilibrium is locally and globally asymptotically stable. Furthermore, we employed a Lyapunov function to analyze the global asymptotic stability of the onchocerciasis — endemic equilibrium whenever [Formula: see text] is greater than unity. In addition, data on mass drug distribution of ivermectin drug to combat onchocerciasis prevalence in Ekiti state of Nigeria were fitted to the model. Graphical results reveal that consistent annual or bi-annual distribution of ivermectin drug in the region is effective in reducing the disease menace. Further simulations also show that public health control measures are needed to minimize infectious contact between humans and blackflies which leads to onchocerciasis infections and visual blindness.

Bifurcation, sensitivity, and optimal control analysis of onchocerciasis disease transmission model with two groups of infectives and saturated treatment function

“…The goal of the controls application is to minimize infective humans with low and high mf parasitic output and blackfly population as well as the total human host population through education campaign together with the cost of controls implementation by the use of possible minimum variable c i , i = 1 … 4. The objective functional (33) includes the number of human infectives with low and high mf parasitic output, total human, and blackfly population together with the cost of personal protection 1 2 M 1 c 2 1 , surgical care 1 2 M 2 c 2 2 , educational campaign for the total human population 1 2 M 3 c 2 3 , and the use of insecticide as vector control, 1 2 M 4 c 2 4 . The quantities H 1 and H 2 denote the cost attached to minimizing the two groups of infectious humans, and the quantities H 3 and H 4 denote the cost attached to minimizing infection in the total human and blackfly population, while the term T * denotes the terminal time period of the control interventions.…”

“…Theorem 5. 49,56 Let (c 1 , c 2 , c 3 , c 4 ) ∈ C be an optimal control quadruple that minimizes the objective functional (33) over C based on the state system (32). Then, the adjoint variables 𝜆 S h , 𝜆 I hl , 𝜆 I hh , 𝜆 T h , 𝜆 S b , and 𝜆 I bl exist, such that the derived Hamiltonian (H t ) is given by…”

“…Moreover, other studies [30][31][32] modeled the disease dynamics of the effect of treatment on onchocerciasis transmission, where they found that the basic reproduction number exhibit backward bifurcation which denote the existence of multiple endemic equilibria and that mass treatment with ivermectin covers a large proportion of population to control the disease, while Idowu and Ogunmiloro 33,34 formulated models governing onchocerciasis disease transmission and investigated the effect of treatment and parametric estimation using data on onchocerciasis predominant in Ekiti State of Nigeria to show that the disease remains endemic unless other forms of measures were scaled up to mitigate the endemicity of the disease in the region. Also, qualitative analysis with the impact of delays were investigated.…”

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

“…Ivermectin can be delivered consistently either annually or biannually in Nigeria, which would effectively lower the risk of illness. In addition, public health management measures are required to reduce the risk of infectious human-blackfly contact, which can result in infections with onchocerciasis and blindness [11]. In South Sudan, the incidence of epilepsy linked to onchocerciasis is predicted to drop significantly by over 50% during the first five years of yearly mass medication administration with at least 70% coverage.…”

Mathematical analysis of a generalized epidemic model with nonlinear incidence function

“…The authors discussed on the division of the human host population into compartments and epidemic interactions between them. Also, several mathematical techniques have been employed by authors to quantitatively and qualitatively describe the dynamics of models of many diseases like onchocerciasis [4,5], conjunctivitis [6], co-infection of malaria with filariasis and toxoplasmosis [7,8], as well as using stability theorems and optimal control analysis to qualitatively and quantitatively analyse epidemic models [9][10][11]. Medical awareness programs through media outlets like radio, electronic prints, television, and social media are means of communicating to the human host community to be aware of how to mitigate disease spread and forestall healthy living [12,13].…”