Abstract

MODELLING AND SIMULATION OF DETERMINISTIC AND STOCHASTIC MODELS OF HEPATITIS B VIRUS TRANSMISSION DYNAMICS INCORPORATING VACCINATION AND TREATMENT AS CONTROLS

1O. Abu and 2P.N. Okolo

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ABSTRACT In this paper, deterministic and stochastic differential equation models of hepatitis B virus transmission dynamics, incorporating vaccination and treatment as control parameters are developed and simulated. The objectives of this study are, first, to compare the solutions of both models and secondly, to investigate the effects of vaccination and treatment on HBV transmission dynamics. The models were solved numerically using Euler and Monte-Carlo methods. The realizations of the stochastic differential equation demonstrate possibility of different disease-prevalence outcomes with the same initial state, a salient feature of which is the possibility of the number of disease carriers reaching a disease-free plateau in absence of control whereas the solution of the deterministic model shows a single disease-prevalence outcome in absence of control. The results also show that, under effective vaccination and treatment, the realizations of the stochastic differential equation and the trajectory of the deterministic model both reach the disease-free plateau within the shortest possible time. However, the mean sample path of the stochastic system is approximately the same as the solution of the deterministic model in both control and out of control scenarios, making the latter a limit solution of the former. Finally, this study suggests that effective vaccination and treatment as a strategy guarantees eradication within the shortest possible time. Key words: Hepatitis B, mathematical model, deterministic model, stochastic model, Wiener Process, diffusion process, stochastic differential equations.

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