Deterministic Threshold Models in the Theory of Epidemics

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.