Bulletin of the American Mathematical Society · 2006 · 382 citations · 61 references
Veterinary MedicineInfectious Disease ControlInfectious DiseasesEpidemiologic MethodsEpidemiologyInfectious Disease EpidemiologyDisease EpidemiologyDisease ModelingDisease SpreadInfectious Disease DynamicsPercolation TheoryTransmission DynamicsBond PercolationCompartmental Disease ModelsContact Network Compartmental ModelsContact Network ModelsDisease TransmissionInfectious Disease ModelsPercolationRandom Graphs
Mathematics has long been an important tool in infectious disease epidemiology. I will provide a brief overview of compartmental models, the dominant framework for modeling disease transmission, and then contact network epidemiology, a more powerful approach that applies bond percolation on random graphs to model the spread of infectious disease through heterogeneous populations. I will derive important epidemiological quantities using this approach and provide examples of its application to issues of public health.
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Emergence of Scaling in Random Networks
Albert-Ĺaszló Barabási, Réka Albert · Science · 1999 · 36.4K citations · Full text
The Mathematics of Infectious Diseases
Herbert W. Hethcote · SIAM Review · 2000 · 6.9K citations