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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)
Using an existing ordinary differential equation model which describes the interaction of the immune system with the human immunodeficiency virus (HIV), we introduce chemotherapy in an early treatment setting through a dynamic treatment and then solve for an optimal chemotherapy strategy. The control represents the percentage of effect the chemotherapy has(More)
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)
While cholera has been a recognized disease for two centuries, there is no strategy for its effective control. We formulate a mathematical model to include essential components such as a hyperinfectious, short-lived bacterial state, a separate class for mild human infections, and waning disease immunity. A new result quantifies contributions to the basic(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 article presents a model for population interactions between an invasive and a native species, where the effect of disturbance in the system (such as flooding) is modeled as a control variable in the growth terms. The motivating example is cottonwood-salt cedar competition, with flooding being detrimental at low and high levels and being advantageous(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)