Discrete Methods in Epidemiology

Studies of the spread and containment of disease rely at heart on a variety of mathematical and computational techniques. This collection aims to introduce the fundamentals of epidemiology and to showcase contemporary work using discrete mathematical techniques. Introductory chapters explain the fundamental concepts of epidemiology, the basic tools provided by mathematics and computer science, and some of the outstanding open problems in the area. Contributed articles then highlight particular problems in monitoring disease outbreaks, vaccination strategies, and modelling disease survival factors, and successfully apply techniques such as formal concept analysis, support vector machines, random graph models, and systems of differential equations. Co-published with the Center for Discrete Mathematics and Theoretical Computer Science beginning with Volume 8. Volumes 1-7 were co-published with the Association for Computer Machinery (ACM). Table of Contents: J. Abello, G. Cormode, D. Fradkin, D. Madigan, O. Melnik, and I. Muchnik -- Selected data mining concepts; D. Schneider -- Descriptive epidemiology: A brief introduction; W. D. Shannon -- Biostatistical challenges in molecular data analysis; L. Hirschman and L. E. Damianos -- Mining online media for global disease outbreak monitoring; D. Ozonoff, A. Pogel, and T. Hannan -- Generalized contingency tables and concept lattices; J. Abello and A. Pogel -- Graph partitions and concept lattices; K. Desai, M.-C. Boily, B. Masse, and R. M. Anderson -- Using transmission dynamics models to validate vaccine efficacy measures prior to conducting HIV vaccine efficacy trials; A. Vazquez -- Causal tree of disease transmission and the spreading of infectious diseases; S. Eubank, V. S. Anil Kumar, M. V. Marathe, A. Srinivasan, and N. Wang -- Structure of social contact networks and their impact on epidemics; J. Abello and M. Capalbo -- Random graphs (and the spread of infections in a social network); S. G. Hartke -- Attempting to narrow the integrality gap for the firefighter problem on trees; J. Li, I. Muchnik, and D. Schneider -- Influences on breast cancer survival via SVM classification in the SEER database; D. Fradkin, I. Muchnik, P. Hermans, and K. Morgan -- Validation of epidemiological models: Chicken epidemiology in the UK; Index. This is a reprint of the 2006 original. (DIMACS/70.S)