Mathematical model of Hepatitis B in the North Tongu District of the Volta Region of Ghana

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Hepatitis B spreads in a host population through direct transmission from the parent to the offspring (vertical transmission) and also through contact with infective individuals (horizontal transmission). In this thesis, we consideedr a mathematical model for the infectious disease (Hepatitis B) and developed a model based on the Susceptible-Infected-Recovered (SIR). The North Tongu District of the Volta Region of Ghana was considered as the host population. The district was assumed to have a constant population size. A system of non-linear differential equations was used to model the spread of the disease in the district. We solveed the system numerically using the forth-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 were completely determined by the basic reproductive number R_0. If R_0<1, the disease-free equilibrium is globally stable and the disease always die out. On the other hand, if R_0>1, an endemic equilibrium exists and was globally stable in the interior of the feasible region, and the disease persists at an endemic equilibrium state if it initially exists.
A thesis submitted to the Department of Mathematics, Kwame Nkrumah University of Science and Technology in partial fulfillment of the requirement for the award of the degree of Master of Philosophy,