Vol. 2, Issue 11, Part D (2016)

Abstract
In this paper, we consider the prediction and the spread of the infectious disease (Hepatitis B) and develop a model based on the Susceptible-Infected-Recovered (SIR). The North Tongu District was considered as the host population. The district is assumed to have a constant population size. A system of non-linear differential equations is used to model the spread of the disease in the district. We solve the system numerically using the fourth-order Runge-Kutta method. Simulation and sensitivity analyses were also performed on the model equations to determine the effect of different parameter values on the spread of the disease. It was shown that the global dynamics are completely determined by the basic reproductive number R₀. If R₀<1, the disease-free equilibrium is globally stable and the disease always dies out. On the other hand, if R₀>1, an endemic equilibrium exists and is globally stable in the interior of the feasible region, and the disease persists in an endemic equilibrium state if it initially exists. This paper indicates that the people of North Tongu would be at high risk if there should be an outbreak of the Hepatitis B. It was therefore recommended that vaccination of the more susceptible populace should to be done, since it will give immunity to the individual