Overall Infectivity Due To Previously Infected Individuals

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.

Value

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

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), weighted by their infectivity at time $t$ (given by the discrete serial interval distribution $w_k$).

In mathematical terms:
$\lambda_t = \sum_{k=1}^{t-1}I_{t-k}w_k$

References

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

Author

Anne Cori

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")