On the existence of invariant domain and local asymptotic behavior of a delayed onchocerciasis model

摘要

In this paper, a mathematical model describing the transmission dynamics of onchocerciasis with distributed delays in infection incubation and recovery in humans and blackfly host population is formulated. We showed that the delayed model is positively invariant and bounded. Also, we obtain the onchocerciasis-free and endemic steady-state solutions as well as the basic reproduction number R-hb of the delayed onchocerciasis model. We found that the delayed onchocerciasis model is locally asymptotically stable whenever R-hb < 1. The findings suggest that, for Rhb to be less than unity, effective use of ivermectin drug for treatment, distribution of treated nets and cloths, etc., is necessary for the minimization and possible elimination of onchocerciasis infection.