This project will develop mathematical and statistical tools to integrate complex, changing connections between infected and susceptible individuals to make simple predictions regarding size and scope of disease outbreaks. An important feature of the dynamics of diseases transmitted on contact is that the contact patterns change in response to infection and progression of symptoms: infected individuals curtail contacts with their regular community due to illness (e.g. being too sick to go to school or work) but increase their contacts with other segments of the population, such as healthcare workers or caretakers in the home. The recent Ebola outbreak in West Africa provides a stark example, but there have been many others, for instance in the waves of HIV-AIDS epidemics in various parts of the world as well as new, smaller outbreaks of Ebola in remote parts of the Congo. Although the question of how evolving contact network structure and infection status affect disease outbreaks seems basic, theoretical treatments have been very limited. The main objective of this project is to help address this knowledge gap by developing mathematical results and tools for simple approximation of these complicated dynamics. The research will be of interest to many individuals and organizations inside and outside of academia including the Centers for Disease Control, the Biomedical Advanced Research and Development Authority, and the Democratic Republic of the Congo Ministry of Public Health. Training will be provided for a PhD student from the Kinshasa School of Public Health via annual monthly visits to Ohio State University and ongoing international collaboration; a US graduate student will also be trained in interdisciplinary research. This project will develop a general Approximate Markovian Computation (AMC) framework for approximating complex stochastic SIR-type disease models on evolving, large, multi-layer networks in which each layer corresponds to an interaction type (also referred to as multiplex or multi-relational network). The idea of AMC is that for a large random configuration network one may often construct Markov jump process closely tracking the outbreak dynamics on the original network despite averaging out some network features (e.g. number of contacts or drop/activation rates). If both processes share the same mean field limiting equations, they also share the same set of limiting parameters; hence the Markov process may also be used for consistent parameter estimation. On the one hand, AMC bears some conceptual resemblance to the popular ABC method in Bayesian inference, although, unlike ABC, it explicitly approximates the likelihood of the SIR process of interest. On the other hand, AMC may also be viewed as a generalization of quasi-equilibrium approximations for stochastic complex systems. In addition to developing relevant theoretical results, the investigators plan to develop software to apply AMC to real field data from contact epidemics in Africa and elsewhere. It is hoped that methods developed in this project will improve predictive modeling for infectious diseases and provide essential insight into key contact epidemic features such as invasion probability, persistence, and outbreak size.