Determining the conditions for the outbreak, spread, and extinction of an infectious disease is an important public health problem. Global eradication of an infectious disease has rarely been achieved, but it continues to be a public health goal for many diseases. More commonly, one can observe local disease extinction, or fade out, followed by a reintroduction of the disease from other regions through a migratory effect. In general, extinction occurs in populations undergoing stochastic effects owing to random transitions. The origins of stochasticity may be internal to the system or may arise from the external environment. Small population size, low contact frequency for frequency-dependent transmission, competition for resources and evolutionary pressure, as well as heterogeneity in populations and transmission, may all be determining factors for extinction to occur. The possibility of an extinction event is affected by the nature and strength of the stochastic noise, as well as other factors, including outbreak amplitude and seasonal phase occurrence. For large populations, the intensity of internal population noise is generally small. However, a rare, large fluctuation can occur with non-zero probability and the system may be able to reach the extinct state. The research objective is to study the dynamics of disease spread and extinction using stochastic metapopulation models that consist of coupled regions or patches. A master equation formalism will be used to understand the disease dynamics and to find the path that maximizes the probability of disease extinction. The results will enable one to speed up disease extinction through the use of control methods including vaccination and quarantine programs.
The proposal is highly multidisciplinary, and involves dynamical systems, stochastic processes, statistical mechanics, and control theory. The mathematical tools that will be developed will provide new ways of analyzing and confirming numerical results. In addition, the analysis will lead to the prediction of novel information and system behavior, and will provide for improved understanding of infectious disease outbreak, spread, and extinction processes. In particular, this new understanding of disease dynamics will enable the development of optimal control methods to lessen disease outbreak and spread. The proposal includes carefully planned projects that will involve and support undergraduate and graduate students in leading-edge research. Significantly, the student population at Montclair State University, and in particular, the Department of Mathematical Sciences, includes a substantial proportion who are members of groups underrepresented in STEM disciplines (including women and minorities) and the research program will leverage existing programs directed to these students. The outcome of the research will be disseminated through seminars, presentations at meetings, and publications in peer-reviewed journals.
