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4. GLOBAL STABILITY ANALYSIS OF THE EFFECT OF VACCINATION AND TREATMENT IN CONTROLLING THE SPREAD OF HEPATITIS B VIRUS WITH INFECTIVE MIGRANTS. by M. A. Nwaokolo,
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GLOBAL STABILITY ANALYSIS OF THE EFFECT OF VACCINATION AND TREATMENT IN CONTROLLING THE SPREAD OF HEPATITIS B VIRUS WITH INFECTIVE MIGRANTS.

M. A. Nwaokolo, A. R. Kimbir, E. S. Onah and T. Aboiyar

Department of Mathematics/Statistics/Computer Science

Federal University of Agriculture, Makurdi, Benue State, Nigeria.

Abstract

In this study, we present a deterministic model on the effect of vaccination and treatment in controlling the spread of hepatitis b virus with infective migrants. The disease free equilibrium state is obtained and we compute the effective reproduction number from which we establish the endemic equilibrium state of the model. The global stability of endemic equilibrium state was analyzed using a lyapunov function and found to be stable. The public health implication is that HBV will be sustained if infective migrants are allowed and also, there is improper or no vaccination regiment, under steady state conditions. Hence the governing model can be applied for predicting the spread of HBV. However, effort should be undertaken that will help to maximize the long-term effectiveness of vaccination and treatment program in curtailing the spread of HBV with infective migrants.

Keywords: Hepatitis B Virus, migrant, vaccination, treatment, stability, Endemic equilibrium state.

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