An Optimal Control Problem for HTLV‐I Infection Model

ABSTRACT In this study, we proposed and analyzed a mathematical model for HTLV‐I infection by considering four populations: healthy CD4+T cells, latently infected CD4+T cells, actively infected CD4+T cells, and HTLV‐I‐specific CD8+T cells. The dynamical behavior of the system is examined both analytically and numerically from the stability and optimal control theory viewpoint. Our model exhibits two biologically feasible equilibrium points, namely, infection‐free and endemic equilibrium points. We explicitly incorporated two control techniques for HTLV‐I infection into the study by considering the corresponding control cost. In the nonconstant control case, we employ Pontryagin's Maximum Principle to determine the necessary conditions for an optimal control strategy of the HTLV‐I infection. It is established and guaranteed that optimal control paths exist for the problem. The uniqueness of our problem's optimal control is also investigated. We used numerical analysis to demonstrate the theoretical analysis and characterize the influence of parameter values on optimal strategy. Our numerical illustrations show that combining two controls are more effective than using a single control.