overall_infectivity {EpiEstim}

Overall Infectivity Due To Previously Infected Individuals

Description

overall_infectivity computes the overall infectivity due to previously infected individuals.

Usage

overall_infectivity(incid, si_distr)

Arguments

incid

One of the following

• A vector (or a dataframe with a single column) of non-negative integers containing an incidence time series

• A dataframe of non-negative integers with two columns, so that incid$local contains the incidence of cases due to local transmission and incid$imported contains the incidence of imported cases (with incid$local + incid$imported the total incidence).

Note that the cases from the first time step are always all assumed to be imported cases.

si_distr

Vector of probabilities giving the discrete distribution of the serial interval.

Details

The overall infectivity \lambda_t at time step t is equal to the sum of the previously infected individuals (given by the incidence vector I, with I = incid$local + incid$imported if I is a matrix), weigthed by their infectivity at time t (given by the discrete serial interval distribution w_k). In mathematical terms:
\lambda_t = \sum_{k=1}^{t-1}I_{t-k}w_k

Value

A vector which contains the overall infectivity \lambda_t at each time step

Author(s)

Anne Cori [e-mail]

References

Cori, A. et al. A new framework and software to estimate time-varying reproduction numbers during epidemics (AJE 2013).

See Also

discr_si, estimate_R

Examples

## load data on pandemic flu in a school in 2009
data("Flu2009")

## compute overall infectivity
lambda <- overall_infectivity(Flu2009$incidence, Flu2009$si_distr)
par(mfrow=c(2,1))
plot(Flu2009$incidence, type = "s", xlab = "time (days)", ylab = "incidence")
title(main = "Epidemic curve")
plot(lambda, type = "s", xlab = "time (days)", ylab = "Infectivity")
title(main = "Overall infectivity")