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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… (More)

- E. Jung, S. Lenhart, Z. Feng, Glenn Webb, Z. FENG
- 2002

Optimal control theory is applied to a system of ordinary differential equations modeling a two-strain tuberculosis model. Seeking to reduce the latent and infectious groups with the resistant-strain tuberculosis, we use controls representing two types of treatments. The optimal controls are characterized in terms of the optimality system, which is solved… (More)

Use of individual-based models (IBMs) has been expanding in both theoretical and applied ecology. IBMs include details at the level of individuals that may lead to different conclusions from aggregated modeling methods. There has been essentially no guidance available on how to most effectively manage populations when the underlying dynamics are best… (More)

We consider a mathematical model of drug therapy for chronic myelogenous leukemia for an individual patient over a fixed time horizon. The disease dynamics are given by a system of ordinary differential equations that describe the interaction between naive T cells, effector T cells and leukemic cancer cells in a hypothetical patient. We introduce two drug… (More)

Arguably one of the most important effects of climate change is the potential impact on human health. While this is likely to take many forms, the implications for future transmission of vector-borne diseases (VBDs), given their ongoing contribution to global disease burden, are both extremely important and highly uncertain. In part, this is owing not only… (More)

This paper considers the optimal control of a degenerate parabolic partial differential equation governing a diusive population with logistic growth terms. Assuming this population causes damage to forest and agricultural land, the optimal control is the trapping rate and the cost functional is a combination of the damage and trapping costs. We prove… (More)

An optimal control problem for an elliptic variational inequality with a source term is considered. The obstacle is the control, and the goal is to keep the solution of the variational inequality close to the desired proole while the H 1 norm of the obstacle is not too large. The addition of the source term strongly aaects the needed compactness result for… (More)

We consider an optimal control problem where the state satisfies a bilateral elliptic varia-tional inequality and the control functions are the upper and lower obstacles. We seek a state that is close to a desired profile and the H 2 norms of the obstacles are not too large. Existence results are given and an optimality system is derived. A particular case… (More)