Simulate SIR data according to a chain Binomial
simulate_SIR_agents(n_sims, n_time_steps, beta, gamma, init_SIR)
| n_sims | number of times to run simulation |
|---|---|
| n_time_steps | number of total time steps (will use 0 to n_time_steps -1 inclusive) |
| beta | infection parameter for SIR chain Binomial. See details |
| gamma | recovery paraemter for SIR chain Binomial. See details |
| init_SIR | vector of (S0, I0, R0) the number of agents initially in the Susceptible, Infected, and Recovered state, respectively. The sum of this will be used as the number of agents |
The the output is a data.frame with columns agent_id, init_state, sim_num, tI, tR. The size is (n_agents x n_sims) x 4.
For each simulation \(i\), agent \(A_{t,k}\) (the kth agent at time t) will update according to the following where the states are denoted \(S=0,I=1,R=2\). The update follows a Bernoulli draw based on the agent's current state. Specifically, $$A_{t,k}| S_{t-1}, I_{t-1} \sim \left \{\begin{array}{ll} \textnormal{Bernoulli} \left ( p_{t-1}\right ) & \textnormal{ if } A_{t-1,k} = 0 \\ 1 + Bernoulli(\gamma) & \textnormal{ if } A_{t-1,k} = 1 \\2 & \textnormal{ otherwise} \end{array} \right . $$ If the agent was infectious at time \(t=0\) then \(tI <= 0 \). If the agent never becomes infectious then \(tI = NA\). If the agent never recovers or is recovered from time 0 on then \(tR = NA\). Otherwise we assume the agent is susceptible.
sims_data <- simulate_SIR_agents(n_sims = 2, n_time_steps = 5, beta = .5, gamma = .1, init_SIR = c(9,1,0)) dim(sims_data)#> [1] 20 4