Epidemics:ferguson2008

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Virtual society Virus spread Literature Version Polish.png
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 (\nu,\psi), and parameters (\theta) is given by:

p(Y,\nu,\psi,\theta) = p(Y|\nu,\psi)p(\nu,\psi|\theta)p(\theta), where

p(\theta), \leftarrow prior level (prior distribution of parameters).
p(\nu,\psi|\theta)=\prod_{ih}^{n_{ih}}p(\nu^{ih},\psi^{ih}|\theta), \leftarrow transmission level
p(Y|\nu,\psi)=\prod_{i}^{n_{ih}}p(Y^{ih}|\nu^{ih},\psi^{ih}), \leftarrow observation level

Y - indicator function: Y_{ij}^{ih}=1 if, for ith, (i=1,2,..,n_{ih}) individual of ihth household (of size n_{ih}) on jth day (j=0,1,..,14), clinical influenza was observed, Y_{ij}^{ih}=0 otherwise.
I^{ih} - group of individuals at ihth household with at least 1 day of clinical influenza, S^{ih} - remaining members of the ihth household.
Z_{i}^{ih} - the 1st day of clinical influenza of ith individual in ihth household
\nu_{i}^{ih},\psi_{i}^{ih} (\nu_{i}^{ih}<\psi_{i}^{ih}) - unobserved variables corresponding to the start end the end of the infectious period for ith individual of ihth household