Mathematical models can provide insights into the dynamics of infectious diseases at both the population and the cellular level. Population models began with Bernoulli in the 18th century with his study of smallpox and have been widely used since 1906 when Ross discovered the vector for malaria and attempted to model its spread. Early in the 20th century, Kermack and McKendrick studied the transmission of infectious agents and in 1927 published the first of their three classical works showing how an epidemic would spread if the density of a host is above a certain threshold. The study of the spread of infectious diseases in a population has continued and we refer the readers to the books of Anderson and May, Mollison, Isham and Medley, Murray, , Castillo-Chavez, and Diekmann.

The application of mathematical models to the cellular aspect of infection began later and in the 1980's we began to see an explosion of models in this area. In the mid 1990's the works of Ho and Perelson, Wei and Nowak and Perelson and Ho helped revolutionize the way the medical community viewed the works of math biologists. In these works was the hypothesis that people infected with HIV where producing billions of viral particles everyday inside their bodies. The hypothesis was determined by a fit of a simple mathematical model to real patient data. The prediction of over a billion viral particles everyday was quite contradictive to what the medical community had assumed. These works were instrumental in the medical communities newly acquired "acceptance" of mathematical models. It opened the doors to newly created positions within medical school for scientists to work on infectious diseases using computer simulations and hence opened a direct connection within departments between modelers and experimentalists. In the past 10 years we have began to see important works in literature that connect modeling with HBV, Chagas Disease, Influenza, tuberculosis, leukemia, and many other diseases. For more general information we recommend the book on Viral Dynamics by Nowak and May.

Here at the University of Michigan we have some of the leaders in the field combining experiment with modeling. Faculty are located in various diverse departments and also in the Center's for MAC-EPID and CSCS.

Research Groups at the University of Michigan

Patrick Nelson (Mathematics)

Kathy Collins (Microbiology, Internal Medicine)

Aaron King (Ecology and Evolutionary Biology)

Center for Molecular and Clinical Epidemiology of Infectious Diseases

Denise Kirschner (Microbiology)

John Younger (Emergency Medicine)

Jim Koopman (School of Public Health)

Carl Simon (Mathematics, Center for the Study of Complex Systems)