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