Mathematical models for the analysis of hepatitis B and AIDS epidemics

Continuous simulation mathematical models are proposed for two different epidemic situations: Hepatitis B in a cohort of newborns followed for life, and one of the danger groups in the current AIDS epidemic. The paper describes the rational behind the systems of differential equations used to model both situations, and the way to test alternative policies, such as vaccination, preventive measures, or the effects of new drugs on AIDS

Simulation of A Mathematical Model Of Hepatitis B Virus Transmission Dynamics In The Presence Of Vaccination And Treatment

In this paper, a mathematical model for the transmission dynamics of hepatitis B virus (HBV) infection incorporating vaccination and treatment as control parameters is presented. The basic reproduction number, , as a threshold parameter, was constructed, in terms of the given model parameters, by the next generation method.   was numerically assessed for its sensitivity to vaccination and treatment parameters. A unique disease-free equilibrium state was determined, indicating possibility of control of HBV disease. The model was solved numerically using Runge-Kutta method of order four to evaluate the effects of vaccination and treatment parameters on the prevalence of the disease. The numerical results of the sensitivity analysis show that increasing either vaccination or treatment rate has the potential of reducing  below unity. The results of the numerical simulations of the model show that effective vaccination, treatment or a combination of both of them as a control strategy can eradicate HBV disease, with the combination being far better than either of them. Finally, these findings strongly suggest that high coverage of vaccination and treatment are crucial to the success of HBV disease control