Disease Dynamics and Epidemic Control on Complex Networks

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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.