A RANDOM GRAPH MODEL FOR THE FINAL-SIZE DISTRIBUTION OF HOUSEHOLD INFECTIONS

✍ Scribed by M. N. ISLAM; C. D. O'SHAUGHNESSY; B. SMITH

• Publisher: John Wiley and Sons
• Year: 1996
• Tongue: English
• Weight: 344 KB
• Volume: 15
• Category: Article
• ISSN: 0277-6715
• DOI: 10.1002/(sici)1097-0258(19960415)15:7/9<837::aid-sim253>3.0.co;2-v

✦ Synopsis

In epidemiological/disease control studies, one might be interested in estimating the parameters community probability infection (CPI) and the household secondary attack rate (SAR), as introduced by Longini and Koopman. The quasi-binomial distribution I (QBD I) with parameters n, p and 0, introduced by Consul, is proposed as a model for the final-size distribution of household infections, where p (CPI) is the probability of an individual being infected from the community and O (SAR) is the rate of secondary transmission of infection within household. An individual can be infected either from within the household or from the community. Let X be the total number of infected members in a household of size n. Then the distribution of X is given by the QBD I with the probability mass function:

P ( X =

X; n, p, 0) = p ( p + xOy-'(1p -X e y , x = 0,1, ... ,n (: > with 0 c p < 1,O 2 0 such that p + ne < 1. The epidemic model is derived from a directed random graph.

Data from influenza epidemics in Asian and American households are used to test the model and a comparison is made with the Longini-Koopman model. It is shown empirically that the QBD I is as good as the L-K model in describing the household infectious disease data, and both models provide almost identical estimates for community and household transmission parameters although they are derived from different perspectives and conditions.