Difference between revisions of "Epidemics:ferguson2008"
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(New page: {{Menu epidemics}} <br/><br/> <br/><br/> An example of so called SIR (Susceptible, Infectious, Recovered) model. Joint probability of observed (''Y''), unobserved variables (<math>\nu,...) |
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<math>p(Y,\nu,\psi,\theta) = p(Y|\nu,\psi)p(\nu,\psi|\theta)p(\theta)</math>, where | <math>p(Y,\nu,\psi,\theta) = p(Y|\nu,\psi)p(\nu,\psi|\theta)p(\theta)</math>, where | ||
<br/><br/> | <br/><br/> | ||
| − | <math>p( | + | <math>p(\theta)</math>, <math>\leftarrow</math> '''prior level''' (prior distribution of parameters). |
<br/> | <br/> | ||
| − | <math>p(\nu,\psi|\theta)=\prod_{ih}^{n_{ih}}p(\nu^{ih},\psi^{ih}|\theta)</math>, | + | <math>p(\nu,\psi|\theta)=\prod_{ih}^{n_{ih}}p(\nu^{ih},\psi^{ih}|\theta)</math>, <math>\leftarrow</math> '''transmission level''' |
| + | <br/> | ||
| + | <math>p(Y|\nu,\psi)=\prod_{i}^{n_{ih}}p(Y^{ih}|\nu^{ih},\psi^{ih})</math>, <math>\leftarrow</math> '''observation level''' | ||
| + | <br/> | ||
| + | |||
| + | ''Y'' - indicator function: <math>Y_{ij}^{ih}=1</math> if, for ''i''th, (<math>i=1,2,..,n_{ih}</math>) individual of ''ih''th household (of size <math>n_{ih}</math>) on ''j''th day (<math>j=0,1,..,14</math>), clinical influenza was observed, <math>Y_{ij}^{ih}=0</math> otherwise. | ||
| + | <br/> | ||
| + | <math>I^{ih}</math> - group of individuals at ''ih''th household with at least 1 day of clinical influenza, <math>S^{ih}</math> - remaining members of the ''ih''th household. | ||
| + | <br/> | ||
| + | <math>Z_{i}^{ih}</math> - the 1st day of clinical influenza of ''i''th individual in ''ih''th household | ||
| + | <br/> | ||
| + | <math>\nu_{i}^{ih},\psi_{i}^{ih} (\nu_{i}^{ih}<\psi_{i}^{ih})</math> - unobserved variables corresponding to the start end the end of the infectious period for ''i''th individual of ''ih''th household | ||
Revision as of 13:37, 20 November 2008
| Virtual society | Virus spread | Literature | Version 
|
|---|---|---|---|
| Polish virtual society epidemics model | |||
| Guinea pigs epidemics model | |||
| Virus genetic evolution epidemics model | |||
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 distribution of parameters).
, transmission level
, observation level
Y - indicator function: 
if, for ith, (
) individual of ihth household (of size 
) on jth day (
), clinical influenza was observed, 
otherwise.
- 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 end the end of the infectious period for ith individual of ihth household
