EAPSI:Building a Mathematical Model of Infectious Disease Spread in Multiple Interacting Communities

Berezovik Irina, Richardson TX

Investigators

Abstract

The spread of infectious diseases can be described by a set of mathematical equations that convey the behavior of the disease in both the short and long term. Accurate mathematical models are used to analyze patterns of disease spread, contributing to more effective prevention and treatment. Models describing the dynamics of infectious diseases in a single community are well researched, but there is little work done on models to analyze the spread of infectious diseases between multiple interacting communities. In the case of China, interactions between densely populated urban groups, such as Beijing/Tianjin, Guangzhou, Shanghai/Hangzhou, and Chengdu provide a good example of such a multi-community model. Multi-community models are becoming so complex as to be difficult to analyze using traditional theoretical methods. This challenge can be overcome by considering the interacting communities as identical and the interactions as symmetric. This award supports research to provide a general framework for such a multi-community model analysis, building on previous work performed at University of Texas Dallas. The research will be conducted under the mentorship of Dr. Yicang Zhou from Xi'an Jiaotong University, who is a world class authority on complex nonlinear models for diseases. The purpose of this project is to apply the equivariant topological degree method to building and studying the symmetric generalizations of the most recently developed epidemiological models of infectious diseases. The generalized models, in which we will be assuming that the interacting communities are identical, will be represented by systems of differential equations with symmetries. In particular, the investigator is interested in analyzing the oscillatory phenomena that may occur when an epidemic equilibrium is destabilized in such a multidimensional system, i.e. there is an appearance of a symmetric Hopf bifurcation. Periodicity of solutions is of the utmost importance to the researcher since it corresponds to the reoccurrence of epidemics, which may exhibit various symmetric properties/patterns. Using the equivariant degree method, supported by computer pro- grams such as GAP, the investigator is planning to perform a direct analysis of such symmetric Hopf bifurcation problems. By computing the equivariant bifurcation invariants, the investigator will provide the full classification of symmetric properties of the bifurcating branches (patterns), which will allow to make predictions for the existence of periodic solutions. This NSF EAPSI award is funded in collaboration with the Ministry of Science and Technology of China.