Integrating stochastic programming, differential equations with deep learning methods for optimizing non-medical intervention policies

新冠肺炎出人意料地袭击了我们的社会。我们没有足够的医疗或疫苗。我们也没有科学的方法来为非医疗干预制定最佳计划，例如关闭、重新开放、个人防护装备(PPE)和优先接种疫苗。为了为下一次大流行(或流行病)做准备，我们需要开发多种量化模型和解决方案方法，以优化这些类型的非医疗干预政策。这种最优化问题需要复杂的数学建模，以准确跟踪围绕人口一级传播和对非医疗干预的反应的疾病传播动态。我的研究计划的长期目标是开发创新和综合的计算模型和算法，以解决与行业应用和疾病传播相关的具有实际意义的问题。针对后者，我们的短期目标(S)将使用随机规划、深度学习和微分方程来生成三个水平(H)集成模型和两个垂直(V)集成数值算法来求解SH1-3：(SH1)计算和生成最优的重启日期集的模型，该模型适应疾病传播动力学的不同多阶段情景；(SH2)优化疫苗接种优先级、时间表和混合的模型，以使我们能够最大化社会经济效益；(SH3)考虑大流行期间的供应链管理和动态需求的最优PPE策略的模型；(SV1)一种新的深度学习方法，用于有效地求解微分方程；(SV2)一种新的深度学习方法，用于生成更准确的疾病传播模型。在所提出的研究中，水平整合SH1-3是专门为抗击大流行而设计的决策模型。他们应该直接提高加拿大政府机构决策过程的质量，以期制定出及时、全面、全面、有弹性和稳健的计划，以应对未来的流行病。鉴于非医疗干预措施发挥的重要作用，拟议的横向模型预计将对加拿大人的健康和国民经济做出重大贡献。垂直积分SV1-2将在深度学习和微分方程组的前沿开发创新的数值算法。它们将立即加快水平集成模型的求解过程，并为其他科学计算模型产生长期价值。我们的综合方法将培养HQP，他们能够进行严格的科学计算，特别是在随机编程、深度学习和微分方程方面，并能够继续就重大决策问题与公共卫生机构进行有效沟通。

COVID-19 hit our society unexpectedly. We did not have sufficient medical treatment or vaccines. Neither did we have scientific approaches to make optimal plans for non-medical interventions, such as shutdowns, reopening, personal protective equipment (PPE), and prioritization of vaccinations. To prepare for the next pandemic (or epidemic), we need to develop multiple quantitative models and solution methodologies to optimize these types of non-medical intervention policies. Such optimization problems require complicated mathematical modeling to accurately track disease transmission dynamics around population-level transmission and reaction to non-medical interventions. The long-term goal of my research program is to develop innovative and integrative computational models and algorithms for solving problems of practical significance relating to industry applications and disease transmission. Addressing the latter, our short-term objectives (S) will use stochastic programming, deep learning and differential equations to generate three horizontally (H) integrated models and two vertically (V) integrated numerical algorithms for solving SH1-3: (SH1) a model that computes and generates an optimal set of reopening dates, which adapts to different multistage scenarios of disease transmission dynamics; (SH2) a model for optimizing vaccination priority, schedules, and mixing such that we can maximize the socioeconomic benefit; (SH3) a model for optimal PPE policy which considers its supply chain management and dynamic demands during a pandemic; (SV1) a new deep learning method to efficiently solve differential equations; and (SV2) a new deep learning method to generate more accurate disease transmission models. In the proposed research, the horizontal integrations SH1-3 are especially designed decision models for combatting a pandemic. They should directly boost the quality of decision-making processes in Canadian government agencies, with a view to working out timely, holistic, comprehensive, resilient, and robust plans when facing future pandemics. Given the significant role played by non-medical interventions, the proposed horizontal models are expected to make a significant contribution to the health and national economy of Canadians. The vertical integrations SV1-2 will develop innovative numerical algorithms at the frontier of deep learning and differential equations. They will immediately speed the solution process of horizontally integrated models, and also generate long-lasting values for other scientific computation models. Our integrative approach will foster HQPs who can carry out rigorous scientific computations, especially on stochastic programming, deep learning and differential equations, and who can go on to effectively communicate with public health agencies on significant decision problems.