On Optimal Control Model for the Treatment of Dual HIV-Parasitoid Pathogen Infection

Abstract

Following the insurmountable and seeming incurable status for the most acclaimed infectious disease – HIV, and which have been worsened by its allies of infectious diseases, this paper projected using ordinary differential equations, a 4-Dimensional mathematical model that accounted for the percentage optimal benefits and the methodological application of chemotherapy - RTI, in the interaction of dual HIV- parasitoid pathogen infectivity with the human immune system. Simple analytical optimal control method was deployed, primed by the maximization of healthy immune system on the basis of control effect of chemotherapy on viruses’ infectivity. Using Pontryagin’s Maximum Principle, the study established the model dynamical optimal control as a composition of system state variables, coupled with four adjoint systems with corresponding initial and transversality conditions together with the optimal control function. The model was solved numerically and results indicated thus: benefits on cost function as highest when onset of infection were followed by high intensity chemotherapy schedule; while optimum control were achieved with prolong treatment administration. The study revealed that optimal control is a function of dynamic optimal weight factor and is independent of prolong treatment duration. The study therefore, advocates the incorporation of dual immunotherapies for the treatment of multiple virus infectivity.