Stability Analysis of a Mathematical Model for Onchocerciaisis Disease Dynamics

Abstract

ABSTRACT:In this work, we propose a Deterministic Mathematical Model that Combines Infectious but not Blind and Infectious Blind Compartments for Onchocerciasis Transmission and Control. Onchocerciasis is usually the term used to describe river blindness, it is a disease that causes blindness, and the second largest cause of blindness after trachoma. It mainly affects the eyes and the skin. The equilibrium states of the model are obtained. The disease free equilibrium state is analysed for stability; the condition for its stability is obtained as an inequality constraint on the parameters. Results shows that although, a 60% treatment coverage rate of infected and infectious blind individuals only is better than 80% treatment coverage rate of infected but not blind individuals only. Also, all the four control strategies reduce the effective reproduction number below unity. A 40% coverage rate of fumigation and treatment of infectious but not blind is better than a 40%coverage rate of fumigation only. It further reveals that a 30% coverage rate of fumigation and treatment of infectious blind is better than 80%coverage rate of fumigation only or fumigation and treatment of infected but not blind only. We are able to show that disease free equilibrium and endemic equilibrium exists and are both locally and globally stable, and we computed the c R of the model and showed that it is a parameter to test for stability, we also use the Jacobi stability technique to show that disease free equilibrium and endemic equilibrium are both locally and globally stable. The sensitivity analysis results shows that the most sensitive parameter is ρ while the least sensitive is v µ , © JASEM https://dx.doi.org/10.4314/jasem.v21i4.6

A Co-Infection Model for Onchocerciasis and Lassa Fever with Optimal Control Analysis

“…In the previous work [19], the co-infection of malaria and Lassa fever was extensively analyzed on the optimal control; however, this work presents a co-infection model for OLF with periodic variational vectors and the model was extended to the optimal control model to analyze the impact of controls, especially in the treatment of infectious humans. This also represents an improvement on some of the studies in [26][27][28][29][30]. The model is qualitatively analyzed using both the model without control and model with control.…”