Abstract

In this paper, a mathematical model for studying dog rabies disease transmission dynamics with vaccination and culling in dog population is developed. Disease free and endemic equilibria were determined and subsequently their local and global stabilities were carried out. Trace-determinant technique is used to determine local stability of disease free equilibrium point while Lyapunov function technique was used to determine global stability of both, disease free and endemic equilibrium points as well as basic reproduction number, R₀. The study findings indicate that, basic reproduction number, R₀, in presence of vaccination and culling is 0.027 while in their absence reached 1.258 which supports the analytical solutions. Biologically, this implies that, the disease is stable to invade and survive more in dog population in the absence of double intervention (vaccination and culling). Also, it is observed that, administering double interventions for atleast 60% rate each, is sufficient to reduce the disease exposed dogs from the peak of 950 to 500 as well as infected from 330 to 130 which eventually will soon clear dog rabies infection spread from the dog population compared to when a single intervention was introduced. Hence, the study recommends the double interventions practice for its efficiency in clearing the disease transmission.

Keywords:Dog rabies; Basic reproduction number; Vaccination