Impute Recovered counts for the SIR model

cases_to_SIR(data, par, method = "chain-binomial")

Arguments

data	data frame or grouped data frame with the following columns t time confirmed number of cumulative confirmed cases at time t in the group N population size, which is used as the number of susceptible (minus the initial infections)
par	named vector of parameters
method	Currently default is "chain-binomial". See details. More methods to come.

Value

the input data with the additional columns

number of susceptible

number of infectious

number of recovered

Details

For the method "chain-binomial". Let the cumulative case counts at time \(t\) be \(J_t\). Then the number of susceptibles is simply \(S_t = N - J_t\). The number of infectious and recovered is imputed iteratively using random draws from a chain binomial based on the state sizes at the previous time step. Specifically, we assume \(I_{t_0} = J_{t_0}\) and \(R_{t_0} = 0\), that is the initial number of recovered individuals is zero. Then for each \( t \in \{ t_0 + 1, t_0 + 2, \dots, T\}\) \(R_t = R_{t-1} +\) Binomial\((I_{t-1}, \gamma)\) and \(I_t = J_t - R_t\). Here \((X0, X1, X2) = (S, I, R)\).

Examples

  df <- data.frame(t = 0:4,
                    confirmed = c(0, 1, 3, 9, 9),
                    N = 10)
   out <- cases_to_SIR(data = df,
                       par = 1)