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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)
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)
A system of ordinary differential equations describes the population dynamics of a rabies epidemic in raccoons. The model accounts for the dynamics of a vaccine, including loss of vaccine due to animal consumption and loss from factors other than racoon uptake. A control method to reduce the spread of disease is introduced through temporal distribution of(More)
An epidemic model for rabies in raccoons is formulated with discrete time and spatial features. The goal is to analyze the strategies for optimal distribution of vaccine baits to minimize the spread of the disease and the cost of implementing the control. Discrete optimal control techniques are used to derive the optimality system, which is then solved(More)
a r t i c l e i n f o a b s t r a c t We formulate an S–I–R (Susceptible, Infected, Immune) spatiotemporal epidemic model as a system of coupled parabolic partial differential equations with no-flux boundary conditions. Immunity is gained through vaccination with the vaccine distribution considered a control variable. The objective is to characterize an(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)
Toxoplasma gondii (T. gondii) is a protozoan parasite that infects a wide range of intermediate hosts, including all mammals and birds. Up to 20% of the human population in the US and 30% in the world are chronically infected. This paper presents a mathematical model to describe intra-host dynamics of T. gondii infection. The model considers the invasion(More)