Disease Dynamics and Epidemic Control on Complex Networks

人类社会和性网络结构在疾病流行的动态中起着重要作用。这对控制或预防流行病的战略具有重大影响。流行病的预防和控制依赖于三个过程：疫苗接种、检测和治疗。我们将开发新的和创新的计算方法，以最优控制复杂网络上的流行病。将使用运筹学方法将资源约束和模型过程结合起来，以实施控制战略。耐抗生素感染是公共卫生领域日益关注的问题。肺炎、淋病和结核病的耐药菌株正变得越来越普遍。在许多情况下，制定有效的控制战略需要疾病模型，在人口结构、地理变异和公共卫生反应差异的背景下，捕捉到药物敏感菌株和耐药菌株共存的情况。这些因素可以使用网络模型来捕获，我们将研究网络上的多菌株疾病模型，以确定耐药菌株如何产生并与其他菌株共存。为了更好地理解复杂网络上的流行病控制，需要异构和动态的模型。异构网络具有两种或两种以上具有不同特征的边。疾病通过每个边缘类型上的接触过程在网络上传播。一个例子是艾滋病毒在注射毒品使用者网络中的传播，其中感染要么通过性接触发生，要么通过共用注射器发生。性网络和注射器共享网络具有不同的拓扑结构。动态网络是根据随机过程进化的，而随机过程通常与节点的疾病过程和状态变化相耦合。连接到一个节点的边可以动态地重新连接到其他节点。这些模型有许多应用，因为一般来说，个人的疾病状态会影响他们的社会行为。此外，可以设计流行病预防和控制方案来改变网络结构，阻止疾病传播。确定这些模型的疫苗接种、检测和治疗资源的最佳分配是具有挑战性的，因为它是一个具有计算昂贵的随机目标函数的约束优化问题。这项研究计划的一个重要方面将是使用真实世界的数据来告知网络模型和公共卫生干预措施的实施。这不仅会导致更现实的模型，还会促进合作，以增强研究的影响。虽然这项研究的动机是在公共卫生方面的应用，但它也对许多其他领域有影响，如社交网络上的信息传播、网络安全、犯罪网络、社交网络营销和物质使用流行病。

Human social and sexual network structure play an important role in the dynamics of disease epidemics. This has significant implications for strategies to control or prevent epidemics. Epidemic prevention and control relies on three processes: vaccination, testing, and treatment. We will develop new and innovative computational methods for optimal control of epidemics on complex networks. An operations research approach will be used to incorporate resource constraints and model processes for implementing control strategies. Antibiotic-resistant infections are of increasing concern in public health. Drug-resistant strains of pneumonia, gonorrhoea, and tuberculosis are becoming more prevalent. In many instances, developing effective control strategies requires disease models which capture coexistence of drug-susceptible and drug-resistant strains in the context of population structure, geographic variability, and differences in public health response. These factors can be captured using network models and we will investigate multi-strain disease models on networks to determine how drug-resistant strains arise and coexist with other strains. A better understanding of epidemic control on complex networks requires models which are both heterogeneous and dynamic. Heterogeneous networks have two or more type of edges with different characteristics. Disease propagates on the network by contact processes on each of the edge types. An example application is HIV transmission on an injection drug user network, in which infection occurs either through sexual contact or by sharing syringes. The sexual and syringe sharing networks have different topology. Dynamic networks evolve according to stochastic processes, which in general are coupled to the disease process and state changes of the nodes. The edges connected to a node may dynamically re-wire to other nodes. These models have many applications, because in general the disease states of individuals impact their social behaviour. Furthermore, epidemic prevention and control programs can be designed to alter the network structure and interdict disease spread. Determining the optimal allocation of vaccination, testing and treatment resources for these models is challenging, because it is a constrained optimization problems with a computationally expensive stochastic objective function. An important aspect of this research program will be to use real-world data to inform both the network models and implementation of public health interventions. This will not only lead to more realistic models, but foster collaborations to enhance the impact of the research. Although motivated by applications in public health, this research also has implications for many other fields, such as information spread on social networks, cyber-security, criminal networks, social network marketing, and substance use epidemics.