library(igraph)
setwd("~/Documents/Violence Cascades/")

# load data
load('Raw Data/lcc.RData')

vic_days = as.numeric(unlist(lcc_verts[,16:21]))
vic_days = vic_days[!is.na(vic_days)]

hist(as.numeric(vic_days,2000,col='lightblue',
     xlab='Day of Study Period',main='Infections During the Study Period')

# get infection counts per day
days = 1:3012
t = table(factor(hyp_lcc_verts$vic.day[vic_ids],levels=days))
counts = as.vector(t)
infs = data.frame(days,counts)

# define background function
fit = function(x, lambda, A, phi) {lambda + A*(sin((2*pi/365.24)*x+phi))}
fit_form = counts ~ lambda + A*(sin((2*pi/365.24)*days+phi))

# explore data
plot(days,counts)
curve(fit(x, lambda=3, A=2, phi=4), add=TRUE ,lwd=4, col="steelblue")

res = nls(formula=fit_form, data=infs, start=list(lambda=3, A=2, phi=4))
co = coef(res); co

plot(t)
plot(days,counts,pch=20,cex=0.9,col='#1f78b4',
     xlab='Day',ylab='Number of Infections')
curve(fit(x, lambda=co["lambda"], A=co["A"], phi=co["phi"]), 
      add=TRUE ,lwd=5, col="#1b9e77")