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A recursive point process model for infectious diseases

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Date
2019
Link to item file
https://hal.archives-ouvertes.fr/hal-01966329
Dewey
Probabilités et mathématiques appliquées
Sujet
Conditional intensity; Contagious diseases; Hawkes process; Productivity
Journal issue
Annals of the Institute of Statistical Mathematics
Publication date
2019
Article pages
31
DOI
http://dx.doi.org/10.1007/s10463-018-0690-9
Forthcoming
oui
URI
https://basepub.dauphine.fr/handle/123456789/18659
Collections
  • CEREMADE : Publications
Metadata
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Author
Schoenberg, Frederic
261085 Department of Statistics, University of California Los Angeles, Los Angeles, CA, United States
Hoffman, Marc
60 CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Harrigan, Ryan
47491 Department of Ecology and Evolutionary Biology [DEEB]
Type
Article accepté pour publication ou publié
Abstract (EN)
We introduce a new type of point process model to describe the incidence of contagious diseases. The model incorporates the premise that when a disease occurs at low frequency in the population, such as in the primary stages of an outbreak, then anyone with the disease is likely to have a high rate of transmission to others, whereas when the disease is prevalent, the transmission rate is lower due to prevention measures and a relatively high percentage of previous exposure in the population. The model is said to be recursive, in the sense that the conditional intensity at any time depends on the productivity associated with previous points, and this productivity in turn depends on the conditional intensity at those points. Basic properties of the model are derived, estimation and simulation are discussed, and the recursive model is shown to fit well to California Rocky Mountain Spotted Fever data.

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