A model for the interaction of HIV with the T CD  4 cells was examined in which an optimal treatment parameter was introduced to control the infectivity termin the HIV dynamic model. The control class was chosen to be a measurable function defined with an objective functional which maximizes the T cell count and minimizes the systemic cost based on the percentage effect of the antiretroviral therapy drug. Optimal control was characterized by applying pontryagin's maximum principle. The values of the objective function at the optimal control shows that the greatest effect do occur when treatment is initiated earliest. Also, results of the numerical simulations indicate that the rate of uninfected T CD  4 increased and virus population decreased due to treatment parameter.

The transmission dynamics of Hepatitis B Virus in a population with infective immigrant is presented with the inclusion of an optimal control strategy to curtail the spread of the virus. To understand the spread of this infection, we develop a mathematical model with control variables of migrant screening and public sensitization. The optimality system is characterized using Pontryagin’s maximum principle and solve numerically with an implicit finite difference method.  Result of the numerical simulation is presented to illustrate the feasibility of this control strategy. The analysis reveals that combination of both control variables could be the most fruitful way to reduce the incidence of Hepatitis B virus.

In this paper, effect of radiation and heat source parameters on temperature, concentration and velocity profile of an electrically conducting fluid passing through an infinite permeable plate is investigated. The governing equation, which was based on the balanced mass, linear momentum, energy and species concentration, were non-dimensionalized to reduce the equations to system of ordinary differential equations. This was then solved by perturbation technique. Effects of radiation parameter, heat source parameter, and Schmidt parameter are analyzed. We observed that the velocity and concentration profiles increase with increase in radiation parameter and heat source parameter. The temperature profile increases with decrease in radiation parameter with increases boundary layer thickness.

The aim of this work is to carry out detailed sensitivity analysis of each parameter in order to know their relative importance in the epidemiological model. This mathematical model for hepatitis B virus is a system of non-linear differential equations which represents the interaction between diseases classes and other epidemiological parameters. The disease free equilibrium points and basic reproduction number of the cases were analyzed using the next generation matrix method.  Sensitivity analysis of with respect to the model parameters was carried out using normalized forward sensitivity index with graphical illustrations for clarity on the effects of these parameters. This analysis showed transmission rate  as the most sensitive parameter which means a reduction to zero of the transmission rate could lead to eradicating HBV infection. It was deduced that sensitivity analysis of these model parameters gives an insight into how best the spread of Hepatitis B Virus could be curtailed.