Mathematical Approaches to Epidemiological Studies of the Emergence, Re-Emergence and Persistence of Infectious Diseases

Mississippi State University, Mississippi State MS

Investigators

Abstract

Li 0078250 The investigator develops mathematical models to investigate several important epidemiological and ecological factors for the emergence, re-emergence and persistence of infectious diseases. The project has three goals: (1) to develop a new mathematical framework in epidemiological modeling that links the human population to its environment, (2) to introduce and develop a new mathematical approach to the analysis of epidemic models, (3) to stimulate mathematical development of more effective analytical and numerical tools for resolving important computational issues arising from the model analysis. The work is carried out along two main themes: Theme I. Develop a mathematical framework in epidemiological modeling using network models that takes into account the full cycle of a disease in nature and encompasses three interconnected key elements: human hosts, intermediate hosts and disease vectors, and environment. Theme II. Develop an approach to the analysis of epidemic models using the method of singular perturbation to further our understanding of several key biological issues such as robust mechanisms for cyclic temporal patterns in disease incidence and the short-term evolution of disease pathogenicity. Computational issues arising from the large scale systems in network models and from the multiple time scales that are inherent in disease transmission processes are also investigated. The global spread of infectious diseases and the emergence of drug-resistant disease agents are causes for alarm at the end of the 20th century. As the world population continues to explode, the world economies continue to become globalized, individual interactions and international travel continues to increase, and the environment around the globe continues to be devastated, the effective control and prevention of the global spread of infectious diseases is destined to be one of the grand challenges facing mankind in the new millennium. Essential to our success in meeting this challenge is a renewed effort in epidemiological studies, a better understanding of the transmission and spread mechanisms of various diseases, and more effective disease control and prevention measures based on these studies and the new understanding. While the nature and scale of the problems at hand inevitably limit the effectiveness of experimental approaches, mathematical modeling has proven to be a valuable approach and an indispensable tool for understanding the problems, for testing hypotheses, and for predicting effective measures of control and prevention. It is expected that results from the project can advance our understanding of the basic ecological and epidemiological mechanisms for the emergence, re-emergence and persistence of infectious diseases and their associated temporal patterns, and improve the present theoretical basis for effective disease control and prevention strategies.