1d:T7c7,# TSIR_LE A function to calculate the Lyapunov Exponennt (LE) from the TSIR model ```r TSIR_LE(time, S, I, alpha, beta, IP) ``` ## Arguments - `time`: The time vector from the data or simulated data - `S`: The S output from the simulated or predicted TSIR model - `I`: The I output from the simulated or predicted TSIR model - `alpha`: The homogeneity parameter from the simulated or predicted TSIR model - `beta`: The inferred contact rate, use beta = contact$beta where contact is an output from runtsir or simulatetsir - `IP`: The generation interval of the pathogen (in weeks) ## Examples ```r ## Not run: require(kernlab) require(ggplot2) require(kernlab) London <- twentymeas$London ## just analyze the biennial portion of the data London <- subset(London, time > 1950) ## define the interval to be 2 weeks IP <- 2 ## first estimate paramters from the London data parms <- estpars(data=London, IP=2, regtype='gaussian',family='poisson',link='log') ## look at beta and alpha estimate plotbeta(parms) ## simulate the fitted parameters sim <- simulatetsir(data=London,parms=parms,IP=2,method='deterministic',nsim=2) ## now lets predict forward 200 years using the mean birth rate, ## starting from rough initial conditions times <- seq(1965,2165, by = 1/ (52/IP)) births <- rep(mean(London$births),length(times)) S0 <- parms$sbar I0 <- 1e-5*mean(London$pop) pred <- predicttsir(times=times,births=births, beta=parms$contact$beta,alpha=parms$alpha, S0=S0,I0=I0, nsim=50,stochastic=T) ## take the last 10 years pred <- lapply(pred, function(x) tail(x, 52/IP * 20) ) ## now compute the Lyapunov Exponent for the simulate and predicted model simLE <- TSIR_LE( time=sim$res$time, S=sim$simS$mean, I=sim$res$mean, alpha=sim$alpha, beta=sim$contact$beta, IP=IP ) predLE <- TSIR_LE( time=pred$I$time, S=pred$S$X3, I=pred$I$X3, alpha=parms$alpha, beta=parms$contact$beta, IP=IP ) simLE$LE predLE$LE ## End(Not run) ```

TSIR_LE function