IP_t: fsMCMC for Epidemic Panel Data
In JMacDonaldPhD/Epidemics: Inference For Epidemics (one line, title case)

View source: R/Sellke_Epidemic_Construction.R

We have a partial panel data observations x* of an epidemic

1	IP_t(beta, gamma, t, U, I)

The epidemic was observed in a subpopulation of m people, at k equaly spaced timepoints between time 0 and time T

The number of Susceptible, Infected and Removed are observed at each timepoint From this the following can be deduced: The number of individuals who ... ... remained susceptible ... became infected being susceptible last time they were observed ... became removed ' '

... remained infected ... became removed after being infected last time they were observed

... remained removed fsMCMC will use data augmentation to make inference on the parameters of the Epidemic process

Non-Centered Selke Construction of an epidemic. A combination of parameter values theta and augmented data Z give the observation of an epidemic Then the probability of observing x* given the constructed empidemic can be calculated and used in an Accept/Reject step

SELLKE CONSTRUCTION

Infectious period Q_i ~ Exp(gamma) = (in D) U_i/gamma ~ Exp(1) i = 1,...,N

Each individual imposes total infectious pressure beta*Q_i over their whole infectious period.

Infectious Thresholds T_i ~ Exp(1/N), N = closed popn size i = 1,...,N

Once this Infectious Threshold is exceeded individual i becomes infected

However, by ordering these threshold times, they can be split up as follows

ordered_T_i = sum_1^(i-1) L_j, L_j ~ Exp((N-j)/N)

So Epidemic is decided by simulating L_1,...,L_N and U_1,...,U_N and beta and gamma.

Neal & Huang used this to construct an epidemic and calculate its final size m

I want the Infection Times, which can then be combined with the infectious periods Q = U/gamma to give the removal times. Then can use transitions_between_observations to obtain N_ss, N_si,..., N_rr.

This is definitely possible.

JMacDonaldPhD/Epidemics documentation built on Jan. 10, 2020, 2:48 a.m.