Optimal HIV treatment by maximising immune response. (English) Zbl 1057.92035

Culshaw, Rebecca V.; Ruan, Shigui; Spiteri, Raymond J.

J. Math. Biol. 48, No. 5, 545-562 (2004).

Summary: We present an optimal control model of drug treatment of the human immunodeficiency virus (HIV). Our model is based upon ordinary differential equations that describe the interaction between HIV and the specific immune response as measured by levels of natural killer cells. We establish stability results for the model. We approach the treatment problem by posing it as an optimal control problem in which we maximise the benefit based on levels of healthy \(CD4+\) \(T\) cells and immune response cells, less the systemic cost of chemotherapy. We completely characterise the optimal control and compute a numerical solution of the optimality system via analytic continuation.

MSC:

92C50	Medical applications (general)
49N90	Applications of optimal control and differential games
49K15	Optimality conditions for problems involving ordinary differential equations
49J15	Existence theories for optimal control problems involving ordinary differential equations

Keywords:

HIV; Immune response; Optimal control; Cytotoxic lymphocytes; Numerical methods

Software:

COLNEW; XPPAUT