Research Initiation Award: Mathematical model of the impact of social behavior in the transmission dynamics of HIV epidemics

研究启动奖为传统黑人学院和大学的初级和中期职业教师提供支持，他们正在建立新的研究项目或重新指导和重建现有的研究项目。期望该奖项有助于进一步提高教师的研究能力和效率，改善其所在机构的研究和教学，并使本科生参与研究经验。诺福克州立大学获得的这一奖项可能在许多领域产生更广泛的影响。该项目将侧重于建立一个数学模型，以调查社会行为在艾滋病毒流行传播动态中的作用。这项工作的结果可以在分析和确定社会行为对艾滋病毒传播的影响时为公共卫生官员提供信息。该项目还将提高诺福克州立大学本科生的研究经验和培训。这个项目将侧重于发展非线性微分方程的确定性系统形式的数学模型，以便定性和定量地分析危险行为对人口中艾滋病毒/艾滋病传播动态的作用。研究已经证实，危险行为与感染艾滋病毒之间存在很强的相关性。其中一些行为与药物滥用有关。虽然人们了解药物滥用有不同程度或阶段，但这种异质性对整个疾病传播过程的影响尚未得到严格研究。该项目将调查这些动态及其在人口中艾滋病毒/艾滋病传播动态中的作用。为了实现这一目标，将开发新的现实的数学模型，其中包括艾滋病毒疾病的基本特征以及相关危险行为的动态。这些模型将使用非线性动力系统的技术（如渐近稳定性和分岔理论）进行严格分析，以深入了解其动态特征，并将使用现有的相关公共卫生和人口统计数据进行参数化。将使用拉丁超立方抽样和偏秩相关系数等适当的抽样技术，对模型的参数进行详细的不确定性和敏感性分析，以评估模拟中使用的参数值估计中的不确定性对所获得的整体模拟结果的影响，并确定驱动疾病传播过程的最重要参数。

Research Initiation Awards provide support for junior and mid-career faculty at Historically Black Colleges and Universities who are building new research programs or redirecting and rebuilding existing research programs. It is expected that the award helps to further the faculty member's research capability and effectiveness, improves research and teaching at her home institution, and involves undergraduate students in research experiences. The award to Norfolk State University has potential broader impact in a number of areas. The project will focus on constructing a mathematical model to investigate the role of social behavior in the transmission dynamics of HIV epidemics. The outcomes of this work can inform public health officials when analyzing and determining the impact of social behavior in the transmission of HIV epidemics. This project will also enhance the research experience and training of undergraduate students at Norfolk State University.This project will focus on developing mathematical models, in the form of deterministic systems of nonlinear differential equations, to qualitatively and quantitatively analyze the role of risky behavior on the transmission dynamics of HIV/AIDS in a population. Studies have established a strong correlation between risky behavior and the acquisition of HIV infection. Some of these behaviors are associated with substance abuse. Although it is understood that there are different degrees or stages of substance abuse, the impact of such heterogeneity on the overall disease transmission process has not been rigorously studied. This project will investigate these dynamics and their role in the transmission dynamics of HIV/AIDS in a population. To achieve this objective, new realistic mathematical models, which incorporate the essential features of HIV disease as well as the dynamics of relevant risky behaviors, will be developed. These models, which will be rigorously analyzed using techniques from nonlinear dynamical systems, such as asymptotic stability and bifurcation theory, to gain insights into their dynamical features, will be parametrized using available relevant public health and demographic data. Detailed uncertainty and sensitivity analysis, using suitable sampling techniques such as Latin Hypercube Sampling and Partial Rank Correlation Coefficients, will be carried out on the parameters of the models to assess the impact of uncertainty in the estimates of the parameter values used in the simulations on the overall simulation results obtained, and determine the most important parameters that drive the disease transmission process.