RUI, Collaborative Research: Optimal Control Studies for Cholera Outbreaks

该霍乱项目的重点是治疗策略，以有效减少细菌霍乱弧菌对感染者造成的临床症状。 控制霍乱爆发的努力，包括口服霍乱疫苗接种，抗生素治疗和卫生工作，被认为是在连续的确定性易感，感染和恢复疾病模型。 该研究团队包括来自默里州立大学、玛丽蒙特大学、旧自治领大学和田纳西大学的高级人员，他们在微分方程的建模、计算和最优控制领域具有专业知识，以及来自这四所大学的多名本科生和研究生。 该团队将通过模拟开发和测试可行的治疗策略，平衡多种控制方案的成本和疗效，并考虑特定年龄的人群和疾病动态。 将研究描述疾病动力学的复杂方程系统中的参数敏感性的复杂性，以及有和没有年龄类的常微分方程和偏微分方程的最优控制策略的数值解和解析解。本研究旨在通过分析微分方程系统，发现可行的疫苗接种和治疗策略，以减轻霍乱疫情。 新的和潜在的转变的概念是最优控制理论应用于相互依赖的方程的调查，以提供战略，有效地减少霍乱疫情的代价，无论是在人类健康和财政负担。 该项目的一个独特之处在于四名女性和一名男性研究人员的合作，他们具有互补的数学背景。 这些人有能力吸引来自全国不同地区的学生。 这些小组的调查结果将通过在地方、区域和国家会议上的介绍以及通过同行审查的出版物传播。 本科生将与来自多个机构的研究生和教师进行持续的研究讨论，因此所取得的进展将同时促进教学，并通过允许垂直整合的协作环境促进每个小组的研究目标。

This cholera project focuses on treatment strategies to effectively reduce the clinical symptoms that the bacterium, Vibrio cholerae, inflicts on infected individuals. Efforts to control a cholera outbreak, including oral cholera vaccination, antibiotic treatment, and sanitation efforts, are considered in successive deterministic susceptible, infected, and recovered disease models. The research team includes senior personnel from Murray State University, Marymount University, Old Dominion University, and the University of Tennessee with expertise in the areas of modeling, computation, and optimal control of differential equations as well as multiple undergraduate and graduate students from the four institutions. The team will develop, and test via simulations viable treatment strategies that balance the cost and efficacy of the multiple control options and that consider age-specific population and disease dynamics. The intricacies of the parameter sensitivities in the systems of complex equations that describe the disease dynamics will be investigated, as well as the numerical and analytic solutions of the optimal control strategies for ordinary and partial differential equations with and without age classes. This study seeks the discovery of viable vaccination and therapeutic strategies to mitigate cholera outbreaks through the analysis of systems of differential equations. The novel and potentially transforming concept is the investigation of optimal control theory applied to the interdependent equations to provide strategies to effectively reduce the costliness of cholera outbreaks both in terms of human wellness and financial burden. A unique aspect of this project is the collaboration of four female and one male investigator with complementary mathematical backgrounds. These individuals have the ability to attract a diverse group of students from different regions of the country. The findings of the teams will be disseminated through presentations at local, regional, and national conferences as well as through peer reviewed publications. The undergraduates will have the benefit of ongoing research discussions with graduate students and faculty from multiple institutions, and thus the advances made will simultaneously promote teaching and facilitate research goals for each group by allowing for a vertically integrated collaborative environment.