Epidemics:ferguson2008
Virtual society | Virus spread | Literature | Version |
---|---|---|---|
Polish virtual society epidemics model | |||
Guinea pigs epidemics model | |||
Virus genetic evolution epidemics model |
Contents
Cauchemez et al Model[1]
An example of so called SIR (Susceptible, Infectious, Recovered) model.
Joint probability of observed (Y), unobserved variables (), and parameters () is given by:
,
where:
, prior level (prior distributions of the parameters of the model).
, transmission level
, observation level
Y - indicator function: (for ith, () individual of ihth household (of size ) on jth day ()), if clinical influenza was observed, otherwise. - all observations from household ihth, Y - observations from all households.
- group of individuals at ihth household with at least 1 day of clinical influenza, - remaining members of the ihth household.
- the 1st day of clinical influenza of ith individual in ihth household
- unobserved variables corresponding to the start and the end of the infectious period for ith individual of ihth household
Observation level - parameters
This level ensured that the unobserved data, , agreed with observed data, Y.
Transmission level - parameters
The instantaneous risk of infection for an individual at time t in household of size n:
,
where - instantaneous risk of infection from the community and within household, respectively.
- the group of infectives just before time t.
The duration of infectious period for ith infective is taken from the gamma distribution with mean and standard deviation .
With the above, conditional on the date of the first infection , we have (for the household):
where I-{1} denotes infectives without the first infected
Prior level
That is prior distributions of all parameters,
References
- ↑ CAUCHEMEZ S, Carrat F, Viboud C, Valleron A J, Boelle P Y, A Bayesian MCMC approach to study transmission of influenza: application to household longitudinal data, Stat. Med., 23, (2004), p3469