Billings The overall objective of this work is to develop a thorough understanding of emergent dynamics in epidemiological models as a practical way to prevent disease outbreaks. Theproject has four parts: 1) developing new, detailed models, with the advantage of analysis by dynamical systems; 2) incorporating time-dependent parameters that more accurately capture climate variability and other nonstationary behavior; 3) adding stochastic perturbations to analyze emergent dynamics; and 4) controlling the system. These problems are studied using theory from dynamical systems, topology, numerical analysis, asymptotics, and stochastic perturbations. In this study, the investigator includes noise, time-dependent parameters, and spatial networks, which are known to combine to produce unexpected complexity in systems, or emergent dynamics. In particular, the investigator builds on recent work developing the Galerkin Transport Matrix, which allows a rigorous study of stochastic dynamics in the context of the topology of the system. This tool can identify precursor behavior to outbreaks, allowing the control of the dynamics by a parameter, such as vaccination, to avoid these patterns and avert epidemics. Disease dynamics have been modeled and studied for hundreds of years. Yet, epidemiologists cannot accurately predict large-scale outbreaks or epidemics in the most common diseases. Currently, there are fears of new strains of deadly diseases and calls for a defensive plan. Questions are being asked about which vaccination or quarantine strategies are necessary to avert outbreaks. Due to ethical issues of testing vaccination strategies on people, epidemiologists must rely on data from past epidemics and corresponding mathematical models to guide these decisions. Models are powerful tools if their results are interpreted correctly. They can capture qualitative dynamics that point to patterns and mechanisms that enable disease persistence in a population. They can also predict the success of an action taken to avert an outbreak. In collaboration with epidemiologists, a better mathematical understanding of the possible dynamics in these models can lead to improved methods of disease control. This work can also be extended to new models to describe the propagation of multiple disease strains and certain types of computer viruses.
|Effective start/end date||1/09/04 → 31/08/08|
- National Science Foundation: $129,969.00