GSE_sim: An epidemic simulation
In BenjamenSimon/EpidemicR: Stochastic modelling and inference for epidemics.

Description Usage Arguments Details Value Examples

This function allows you to simulate a stochastic SIR epidemic, with a heterogeneous contact matrix.

1	GSE_sim(N, beta.mat, gamma)

`N`	The size of the population.
`beta.mat`	An NxN matrix of the pair wise infection rates between all individuals.
`gamma`	The removal rate.

The infectious life history of each individual is comprised of two parts;

Q_i, the length of individuals i's infectious period.
W_{i,j}, the length of time, after individual i becomes infected, before they make contact with individual j.

The distributions of which are given by;

Q_i ~ Exp(gamma).
W_{i,j} ~ Exp(beta_{i,j}).

The simulation begins with an initial infective infectious at time 0.

I_i is the time at which individual i becomes infected, and their removal time is given by R_i = I_i + Q_i.

If W_{i,j} < Q_i, then individual i makes infectious contact with individual j at time I_i + W_{i,j}.

If individual j is susceptible when this happens, then they become infected, otherwise nothing happens. The simulation assumes that W_{i,j} != W_{j,i}.

The simulation continues until there are no infected individuals left in the population.

The function returns a matrix containing 4 columns; the id number of each individual, their infection time (NA if not infected), their removal time (NA if not infected), and their generated infectious period length.

# Generate a distance matrix
   distance_mat <- Dist_mat_unif(N=100, xlim = 20, ylim = 20)[[2]]

# Generate an associated infection rate rate matrix
   rate_mat <- Beta_mat_form(distance_mat, c(0.004, 0.002), 10)
   
# Generate a simulated epidemic
   Hetero_sim <- GSE_sim(N = 100, beta.mat = rate_mat, gamma = 0.15)