Mathematical Modeling of Infectious Diseases

Professor Herbert Hethcote

Department of Mathematics
University of Iowa

March 8, 1996

Abstract

Differential equation models can be used to describe the dynamics of the spread of an infectious disease between infectives and susceptibles in a community. When there is disease-acquired immunity, then vaccine-acquired immunity is also possible. Levels of vaccination necessary to achieve group immunity for measles, rubella, polio, chickenpox, etc will be estimated. Some alternative mathematical models with features such as variable population size and time delays will be formulated and discussed.