Mathematical Structures of Epidemic Systems

Mathematical modelling of communicable diseases has in the past two decades been the subject of intense research activity, on the part of both epidemiologists and biomathematicians. Nonlinear forces of infection, spatial structure, age structure and other relevant features have been integrated to make the models more and more realistic and useful in prediction and control. The author's perspective in this book is that there is a concrete possibility of classifying most of the available models according to their mathematical structure, to obtain a solid framework for analyzing the behaviour of the modelled epidemic systems. This monograph suggests a possible classification of a large amount of models (bilinear, nonlinear, with or without structure), based on the Lyapunov stability theory and the theory of preserving dynamical systems. The volume contains an original presentation of many worked out examples and case studies, mainly based on the author's experience, fully integrated with the exposition of the theory. It also contains a review of the most recent advances in the modelling of epidemics, including HIV/AIDS.