Control Theory Commons^™

Managing Multi-Drug Resistance: An Evolutionary Game Theory And Optimal Control Approach, Shukhrat Nasrulloev

Theses and Dissertations

Multi-drug resistance is an evolutionary process in which treatment eliminates sensitive cells, allowing resistant clones to dominate. This thesis investigates this process using a framework integrating population dynamics, evolutionary game theory, and optimal control theory. We develop a two-population logistic growth model describing competition between drug-sensitive and drug-resistant cells under treatment, construct dose-dependent payoff matrices and replicator dynamics to characterize evolutionary competition, and derive a critical drug level D_crit = (r_S - rR)/(dS - d_R) at which resistant cells gain a fitness advantage. An optimal control problem is formulated via Pontryagin's Maximum Principle to identify schedules …

Application Of Optimal Control Theory To A Malaria Model, Cassidy Hill

Murray State Theses and Dissertations

With malaria still prevalent and considered to be one of the most devastating infectious diseases in the world, many scientific efforts have been made to reduce its impact. One such effort includes the construction of mathematical models. Mathematical models can be used to analyze malaria transmission dynamics in the human population. The development of these models allows researchers to consider the control measures necessary to reduce the prevalence of malaria infection and possibly eliminate it.

The model presented in this thesis will provide the relationship of female Anopheles mosquitoes and insecticide treated paint acting as the control. A deterministic system …

Target Control Of Networked Systems, Isaac S. Klickstein

Mechanical Engineering ETDs

The control of complex networks is an emerging field yet it has already garnered interest from across the scientific disciplines, from robotics to sociology. It has quickly been noticed that many of the classical techniques from controls engineering, while applicable, are not as illuminating as they were for single systems of relatively small dimension. Instead, properties borrowed from graph theory provide equivalent but more practical conditions to guarantee controllability, reachability, observability, and other typical properties of interest to the controls engineer when dealing with large networked systems. This manuscript covers three topics investigated in detail by the author: (i) the …