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Chapter 7 Criticality in epidemiology

Nico Stollenwerk

Universidade do Porto, Faculdade de Ciencias, Departamento de Matematica Pura,Rua do Campo Alegre, 687, 4169-007 Porto, Portugal and

Gulbenkian Institute of Science, Apartado 14, Edificio Amerigo Vespucci, 2781-901 Oeiras, Portugal [email protected]

Vincent A.A. Jansen School of Biological Sciences, Royal Holloway, University of London, Egham, Surrey TW20 0EX, UK

For a long time criticality has been considered in epidemiological models. We review the body of theory developed over the last twenty five years for the simplest models. It is at first glance difficult to imagine that an epidemiological system operates at a very fine tuned critical state as opposed to any other parameter region. However, the advent of self-organized criticality has given hints in how to interpret large fluctuations observed in many natural systems including epidemiological systems. We show some scenarios where criticality has been observed (e.g., measles under vaccination) and where evolution towards a critical state can explain fluctuations (e.g., meningococcal disease.)

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