These notes correspond to a set of lectures given at the Univer sity of Alberta during the spring semester, 1973. The first four sec tions present a systematic development of a deterministic, threshold model for the spraad of an infection. Section 5 presents some compu tational results and attempts to tie the model with other mathematics. In each of the last three sections a separate, specialized topic is presented. The author wishes to thank Professor F. Hoppensteadt for making available preprints of two of his papers and for reading and comment ing on a preliminary version of these notes. He also wishes to thank Professor J. Mosevich for providing the graphs in Section 5. The visit at the University of Alberta was a very pleasant one and the author wishes to express his appreciation to Professors S. Ghurye and J. Macki for the invitation to visit there. Finally, thanks are due to the very competent secretarial staff at the University of Alberta for typing the original draft of the lecture notes and to Mrs. Ada Burns of the University of Iowa for her excellent typescript of the final version. TABLE OF CONTENTS 1. A Simple Epidemic Model with Permanent Removal . . . • . . . 1 2. A More General Model and the Determination of the Intensity of an Epidemic. 10 21 3. A Threshold Model. 4. A Threshold Model with Temporary Immunity. 34 5. Some Special Cases and Some Numerical Examples 48 A Two Population Threshold Model . 62 6.

This timely book covers the basic concepts of the dynamics of epidemic disease, presenting various kinds of models as well as typical research methods and results. It introduces the latest results in the current literature, especially those obtained by highly rated Chinese scholars. A lot of attention is paid to the qualitative analysis of models, the sheer variety of models, and the frontiers of mathematical epidemiology. The process and key steps in epidemiological modeling and prediction are highlighted, using transmission models of HIV/AIDS, SARS, and tuberculosis as application examples.

Based on lecture notes of two summer schools with a mixed audience from mathematical sciences, epidemiology and public health, this volume offers a comprehensive introduction to basic ideas and techniques in modeling infectious diseases, for the comparison of strategies to plan for an anticipated epidemic or pandemic, and to deal with a disease outbreak in real time. It covers detailed case studies for diseases including pandemic influenza, West Nile virus, and childhood diseases. Models for other diseases including Severe Acute Respiratory Syndrome, fox rabies, and sexually transmitted infections are included as applications. Its chapters are coherent and complementary independent units. In order to accustom students to look at the current literature and to experience different perspectives, no attempt has been made to achieve united writing style or unified notation. Notes on some mathematical background (calculus, matrix algebra, differential equations, and probability) have been prepared and may be downloaded at the web site of the Centre for Disease Modeling (www.cdm.yorku.ca).

This collection of papers gives a representative cross-selectional view of recent developments in the field. After a survey paper by C. Lefèvre, 17 other research papers look at stochastic modeling of epidemics, both from a theoretical and a statistical point of view. Some look more specifically at a particular disease such as AIDS, malaria, schistosomiasis and diabetes.

This IMA Volume in Mathematics and its Applications MATHEMATICAL APPROACHES FOR EMERGING AND REEMERGING INFECTIOUS DISEASES: MODELS, AND THEORY METHODS is based on the proceedings of a successful one week workshop. The pro ceedings of the two-day tutorial which preceded the workshop "Introduction to Epidemiology and Immunology" appears as IMA Volume 125: Math ematical Approaches for Emerging and Reemerging Infectious Diseases: An Introduction. The tutorial and the workshop are integral parts of the September 1998 to June 1999 IMA program on "MATHEMATICS IN BI OLOGY. " I would like to thank Carlos Castillo-Chavez (Director of the Math ematical and Theoretical Biology Institute and a member of the Depart ments of Biometrics, Statistics and Theoretical and Applied Mechanics, Cornell University), Sally M. Blower (Biomathematics, UCLA School of Medicine), Pauline van den Driessche (Mathematics and Statistics, Uni versity of Victoria), and Denise Kirschner (Microbiology and Immunology, University of Michigan Medical School) for their superb roles as organizers of the meetings and editors of the proceedings. Carlos Castillo-Chavez, es pecially, made a major contribution by spearheading the editing process. I am also grateful to Kenneth L. Cooke (Mathematics, Pomona College), for being one of the workshop organizers and to Abdul-Aziz Yakubu (Mathe matics, Howard University) for serving as co-editor of the proceedings. I thank Simon A. Levin (Ecology and Evolutionary Biology, Princeton Uni versity) for providing an introduction.