# Simulate Count Time Series with Outbreaks

`sts_creation.Rd`

Function for simulating a time series and creating an
`sts`

object.
As the counts are generated using a negative binomial distribution
one also gets the (1-alpha) quantile for each timepoint (can be interpreted
as an in-control upperbound for in-control values).
The baseline and outbreaks are created as in Noufaily et al. (2012).

## Usage

```
sts_creation(theta, beta, gamma1, gamma2, m, overdispersion, dates,
sizesOutbreak, datesOutbreak, delayMax, alpha, densityDelay)
```

## Arguments

- theta
baseline frequency of reports

- beta
time trend

- gamma1
seasonality

- gamma2
seasonality

- m
seasonality

- overdispersion
`size`

parameter of`rnbinom`

for the parameterization with mean and dispersion- dates
dates of the time series

- sizesOutbreak
sizes of all the outbreaks (vector)

- datesOutbreak
dates of all the outbreaks (vector)

- delayMax
maximal delay in time units

- alpha
alpha for getting the (1-alpha) quantile of the negative binomial distribution at each timepoint

- densityDelay
density distribution for the delay

## References

Noufaily, A., Enki, D.G., Farrington, C.P., Garthwaite, P., Andrews, N.J., Charlett, A. (2012): An improved algorithm for outbreak detection in multiple surveillance systems. Statistics in Medicine, 32 (7), 1206-1222.

## Examples

```
set.seed(12345)
# Time series parameters
scenario4 <- c(1.6,0,0.4,0.5,2)
theta <- 1.6
beta <- 0
gamma1 <-0.4
gamma2 <- 0.5
overdispersion <- 1
m <- 1
# Dates
firstDate <- "2006-01-01"
lengthT=350
dates <- as.Date(firstDate) + 7 * 0:(lengthT - 1)
# Maximal delay in weeks
D=10
# Dates and sizes of the outbreaks
datesOutbreak <- as.Date(c("2008-03-30","2011-09-25"))
sizesOutbreak <- c(2,5)
# Delay distribution
data("salmAllOnset")
in2011 <- which(isoWeekYear(epoch(salmAllOnset))$ISOYear == 2011)
rT2011 <- salmAllOnset@control$reportingTriangle$n[in2011,]
densityDelay <- apply(rT2011,2,sum, na.rm=TRUE)/sum(rT2011, na.rm=TRUE)
# alpha for the upperbound
alpha <- 0.05
# Create the sts with the full time series
stsSim <- sts_creation(theta=theta,beta=beta,gamma1=gamma1,gamma2=gamma2,m=m,
overdispersion=overdispersion,
dates=dates,
sizesOutbreak=sizesOutbreak,datesOutbreak=datesOutbreak,
delayMax=D,densityDelay=densityDelay,
alpha=alpha)
plot(stsSim)
```