Geodesic
Optimizing chemotherapy in an HIV model.
Electronic journal of differential equations, Tome 1998 (1998)
We examine an ordinary differential system modeling the interaction of the HIV virus and the immune system of the human body. The optimal control represents a percentage effect the chemotherapy has on the interaction of the $CD4^{+}$T cells with the virus. We maximize the benefit based on the T cell count and minimize the systemic cost based on the percentage of chemotherapy given. Existence of an optimal control is proven, and the optimal control is uniquely characterized in terms of the solution of the optimality system, which is the state system coupled with the adjoint system. In addition, numerical examples are given for illustration.
Classification : 34B15, 49K15, 92D30
Keywords: chemotherapy, HIV, optimal control 
@article{EJDE_1998__1998__a30,
     author = {Fister,  K. Renee and Lenhart,  Suzanne and McNally,  Joseph Scott},
     title = {Optimizing chemotherapy in an {HIV} model.},
     journal = {Electronic journal of differential equations},
     year = {1998},
     volume = {1998},
     zbl = {1068.92503},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_1998__1998__a30/}
}
TY  - JOUR
AU  - Fister,  K. Renee
AU  - Lenhart,  Suzanne
AU  - McNally,  Joseph Scott
TI  - Optimizing chemotherapy in an HIV model.
JO  - Electronic journal of differential equations
PY  - 1998
VL  - 1998
UR  - http://geodesic.mathdoc.fr/item/EJDE_1998__1998__a30/
LA  - en
ID  - EJDE_1998__1998__a30
ER  - 
%0 Journal Article
%A Fister,  K. Renee
%A Lenhart,  Suzanne
%A McNally,  Joseph Scott
%T Optimizing chemotherapy in an HIV model.
%J Electronic journal of differential equations
%D 1998
%V 1998
%U http://geodesic.mathdoc.fr/item/EJDE_1998__1998__a30/
%G en
%F EJDE_1998__1998__a30
Fister,  K. Renee; Lenhart,  Suzanne; McNally,  Joseph Scott. Optimizing chemotherapy in an HIV model.. Electronic journal of differential equations, Tome 1998 (1998). http://geodesic.mathdoc.fr/item/EJDE_1998__1998__a30/