MATHEMATICAL MODELLING OF HEPATITIS B VIRUS WITH INFECTIOUS LATENT

Abstract

ABSTRACT In this research, a mathematical model for the transmission dynamics of Hepatitis B virus (HBV) incorporating treatment, using condom and vaccine as the control parameters, incorporating vaccinated compartment was formulated. It was assumed that a susceptible individual can get infected with HBV when there is an effective interaction with any of the three infectious classes: exposed, chronic or acute individuals. The basic reproduction number was obtained using the next generation matrix approach. The Jacobian stability technique and the Lyaponuv second method of stability were used to establish the local and global stabilities of the equilibrium states respectively. The stability analysis shows that HBV can be eradicated from the entire population when 0 1 R  but will continue to persevere within the population when 0 1 R  . The model was solved analytically using the homotopy perturbation method (HPM), and the stability analysis was verified with graphs using maple 18. The result shows that vaccination have a significant impact on all the compartments, but treatment only have effect on the infected compartments. It is therefore recommended that every susceptible individual to HBV should get vaccinated, and those who are acutely and chronically infected should receive early medical attention.