Epidemics:ferguson2008 - Revision history

Magd: /* Prior level */

2008-11-25T14:06:28Z

‎Prior level

Magd: /* Transmission level - parameters \alpha,\,\varepsilon,\,\beta,\,(\eta) */

2008-11-21T11:56:47Z

‎Transmission level - parameters \alpha,\,\varepsilon,\,\beta,\,(\eta)

Magd: /* Prior level */

2008-11-20T18:22:23Z

‎Prior level

Magd: /* Transmission level */

2008-11-20T18:21:40Z

‎Transmission level

Magd: /* Cauchemez et al ModelCAUCHEMEZ 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 */

2008-11-20T18:16:27Z

‎Cauchemez et al ModelCAUCHEMEZ 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

Magd: /* Observation level - parameters \nu,\,\psi */

2008-11-20T17:41:53Z

‎Observation level - parameters \nu,\,\psi

Magd: /* Cauchemez et al ModelCAUCHEMEZ 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 */

2008-11-20T17:41:01Z

Magd: /* Observation level */

2008-11-20T17:40:33Z

‎Observation level

Magd at 17:39, 20 November 2008

2008-11-20T17:39:40Z

Magd at 14:20, 20 November 2008

2008-11-20T14:20:36Z

@@ Line 63: / Line 63: @@
 That is prior distributions of all parameters, <math>\theta=(\mu, \sigma, \alpha, \beta, \varepsilon, \eta)</math>
 == References ==
 <references/>

@@ Line 40: / Line 40: @@
 This level ensured that the unobserved data, <math>\nu,\,\psi</math>, agreed with observed data, ''Y''.
-=== Transmission level - parameters <math>\alpha,\,\varepsilon,\,\beta,\,(\eta)</math> ===
+=== Transmission level - parameters <math>\alpha,\,\varepsilon,\,\beta,\,(\eta),\,\mu,\,\sigma</math> ===
 The instantaneous risk of infection for an individual at time ''t'' in household of size ''n'':
@@ Line 47: / Line 47: @@
 <br/>
 <br/>where <math>\alpha, \varepsilon</math> - instantaneous risk of infection from the community and within household, respectively.
-The duration of infectious period for ''i''th infective <math>d_i=\psi_i-\nu_i</math> is taken from gamma distribution with mean <math>\mu_i</math> and standard deviation <math>\sigma_i</math>
+The duration of infectious period for ''i''th infective <math>d_i=\,\psi_i-\nu_i</math> is taken from the gamma distribution with mean <math>\mu_i</math> and standard deviation <math>\sigma_i</math>.
 === Prior level ===

@@ Line 53: / Line 53: @@
-That is prior distribution of parameters, <math>\theta=(\mu, \sigma, \alpha, \beta, \varepsilon, \eta)</math>
+That is prior distributions of all parameters, <math>\theta=(\mu, \sigma, \alpha, \beta, \varepsilon, \eta)</math>
 == References ==
 <references/>

@@ Line 40: / Line 40: @@
 This level ensured that the unobserved data, <math>\nu,\,\psi</math>, agreed with observed data, ''Y''.
-=== Transmission level ===
+=== Transmission level - parameters <math>\alpha,\,\varepsilon,\,\beta,\,(\eta)</math> ===
 The instantaneous risk of infection for an individual at time ''t'' in household of size ''n'':
@@ Line 49: / Line 49: @@
 The duration of infectious period for ''i''th infective <math>d_i=\psi_i-\nu_i</math> is taken from gamma distribution with mean <math>\mu_i</math> and standard deviation <math>\sigma_i</math>
 === Prior level ===

@@ Line 14: / Line 14: @@
 <br/> where:
 <br/><br/>
-<math>p\big(\theta\big)</math>, <math>\leftarrow</math> '''prior level''' (prior distribution of the parameters of the model).
+<math>p\big(\theta\big)</math>, <math>\leftarrow</math> '''prior level''' (prior distributions of the parameters of the model).
 <br/>
 <math>p(\nu,\psi|\theta)=\prod_{ih}^{n_{ih}}p(\nu^{ih},\psi^{ih}|\theta)</math>, <math>\leftarrow</math> '''transmission level'''

@@ Line 33: / Line 33: @@
 <math>
 p(Y|\nu,\psi)=\left\{\begin{array}{ll}
-, & \textrm{if\,for\,all\,infected\;}i\,(i\in I): \nu_i\in [Z_i-3,Z_i] \land \nu_i < \psi_i\\
+, & \textrm{if\;for\;all\;infected\;}i\,(i\in I): \nu_i\in [Z_i-3,Z_i] \land \nu_i < \psi_i\\
 , & \textrm{otherwise}
 \end{array} \right.

@@ Line 4: / Line 4: @@
 <br/><br/>
-=== Cauchemez et al Model<ref name="cauchemez2004">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</ref> ===
+== Cauchemez et al Model<ref name="cauchemez2004">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</ref> ==
 An example of so called SIR (Susceptible, Infectious, Recovered) model.
@@ Line 28: / Line 28: @@
 <br/><br/>
 <math>\nu_{i}^{ih},\psi_{i}^{ih} (\nu_{i}^{ih}<\psi_{i}^{ih})</math> - unobserved variables corresponding to the start and the end of the infectious period for ''i''th individual of ''ih''th household
-−
 === Observation level - parameters <math>\nu,\,\psi</math> ===