The objective of this proposal is to develop new mathematical models of infectious disease transmission that effectively, capture the impact of stochasticity on dynamics and lead to more effective control. The group will study the dynamics of disease spread in fluctuating environments modeled at various population scales. First, the group will develop a new class of stochastic metapopulation models for disease spread, noting the importance of stochastic effects in the dynamics. These models capture new types of solutions that cannot be realized in deterministic models, such as disease extinction. The group proposes to develop new mathematical and computational methods for designing and analyzing this class of models. The group will also model various delivery schedules of vaccines into populations. By assuming limited resources, such as constrained vaccine supply or quarantine-type contact control, the results from these models will lead to practical solutions for experimentalists and poUcy makers. The project will lead to greater insight into the mechanisms that allow a disease to successfully propagate in a population, as well as new mathematical tools to analyze stochastic systems. In our long term vision for this project, the group will contribute new mathematical tools to the field of epidemiology. These tools will be motivated by improved models of real world problems, which lead to better ways to design optimization methods. Our work is driven by real epidemiological threats, is derived from data collected from around the world, and is focused on answering questions that could save lives. There is an excitement about the impact of interdisciplinary research efforts combining mathematical fields, such as nonlinear analysis, stochastic d3Tiamics, and network theory, with systems biology approaches such as population dynamics, epidemiology, and immunology. This proposal describes ways in which modeling can open new research directions in all of these fields.
Noting the collaborative nature of this research proposal, we expect that this project will produce findings that could improve health standards across the world. It may lead to improved methods of disease control and health monitoring.
| Forgoston, Eric; Shaw, Leah B; Schwartz, Ira B (2015) A Framework for Inferring Unobserved Multistrain Epidemic Subpopulations Using Synchronization Dynamics. Bull Math Biol 77:1437-55 |
| Rodriguez-Barraquer, Isabel; Mier-y-Teran-Romero, Luis; Schwartz, Ira B et al. (2014) Potential opportunities and perils of imperfect dengue vaccines. Vaccine 32:514-20 |
| Shkarayev, Maxim S; Tunc, Ilker; Shaw, Leah B (2014) Epidemics with temporary link deactivation in scale-free networks. J Phys A Math Theor 47: |
| Tunc, Ilker; Shaw, Leah B (2014) Effects of community structure on epidemic spread in an adaptive network. Phys Rev E Stat Nonlin Soft Matter Phys 90:022801 |
| Rodriguez-Barraquer, Isabel; Mier-y-Teran-Romero, Luis; Burke, Donald S et al. (2013) Challenges in the interpretation of dengue vaccine trial results. PLoS Negl Trop Dis 7:e2126 |
| Shkarayev, Maxim S; Shaw, Leah B (2013) Asymptotically inspired moment-closure approximation for adaptive networks. Phys Rev E Stat Nonlin Soft Matter Phys 88:052804 |
| Shkarayev, Maxim S; Schwartz, Ira B; Shaw, Leah B (2013) Recruitment dynamics in adaptive social networks. J Phys A Math Theor 46:245003 |
| Lindley, Brandon; Mier-Y-Teran-Romero, Luis; Schwartz, Ira B (2013) Noise Induced Pattern Switching in Randomly Distributed Delayed Swarms. Proc Am Control Conf 2013:4587-4591 |
| Forgoston, Eric; Schwartz, Ira B (2013) Predicting unobserved exposures from seasonal epidemic data. Bull Math Biol 75:1450-71 |
| Mier-y-Teran-Romero, Luis; Schwartz, Ira B; Cummings, Derek A T (2013) Breaking the symmetry: immune enhancement increases persistence of dengue viruses in the presence of asymmetric transmission rates. J Theor Biol 332:203-10 |
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