# Citation: Sanchez, J.N. and B.R. Hudgens. Impacts of Heterogeneous Host Densities and Contact Rates on Pathogen Transmission in the Channel Island Fox (Urocyon littoralis). Biological Conservation. 2019.

# Jessica N. Sanchez
# jnsanchez@ucdavis.edu
# Institute for Wildlife Studies 
# P.O. Box 1104
# Arcata, CA 95518

# Brian R. Hudgens
# hudgens@iws.org
# Institute for Wildlife Studies 
# P.O. Box 1104
# Arcata, CA 95518


########################## RABIES ##########################


#VARIABLES - PERMANENT VECTORS WITHIN EACH RUN
#sim = number of simulations to run
#target.N = number of homes to attempt to generate
#N = number of home ranges actually generated
#X = size of island x axis
#Y = size of island y axis                         
#fox = fox ID number
#x = fox x coordinate
#y = fox y coordinate
#radius = radius of fox circular home range
#HR.area = area of fox home range
#habitat = habitat type of fox based on y coordinate
#time = number of time-steps
#resample.N = number of simulations to run between resampling home ranges
#summary.density = density of foxes in each habitat type during each simulation
#transmission.probability = probability of pathogen transmission given contact between S and I fox
#potential.seeds = all foxes with min/max y values
#seed = random sample of foxes in potential.seeds
#new.latents = number of new latent animals at each time-step
#infectives = which foxes are infectious at time t-1? 
#random.sample = random numbers to compare against transmission probabilities
#total.0 = sum of all susceptible foxes at each time-step
#total.1 = sum of all infectious foxes at each time-step
#total.2 = sum of all latent foxes at each time-step
#total.3 = sum of all removed foxes at each time-step 
#total.4 = sum of all vaccinated foxes at each time-step
#status.totals.at.end = sum of all foxes in each disease class at last time-step
#summary.total.0 = number of suceptible foxes at each time step in each simulation
#summary.total.1 = number of latent foxes at each time step in each simulation
#summary.total.2 = number of infectious foxes at each time step in each simulation
#summary.total.3 = number of removed foxes at each time step in each simulation
#summary.total.4 = number of vaccinated foxes at each time step in each simulation
#summary.total.i = mean number of susceptible foxes at each time-step (averaged across simulations)
#total.0.means = mean number of susceptible foxes at each time-step (averaged across simulations)
#total.1.means = mean number of latent foxes at each time-step (averaged across simulations)
#total.2.means = mean number of infectious foxes at each time-step (averaged across simulations)
#total.3.means = mean number of removed foxes at each time-step (averaged across simulations)
#total.4.means = mean number of vaccinated foxes at each time-step (averaged across simulations)
#total.i.means = mean number of infected foxes at each time-step (averaged across simulations)
#Rs = Re at each time-step
#Ro = number of secondary infections caused by seed fox in each simulation
#spread = distance between seed fox and furthest infected fox (I or L) at each time-step
#latent.period = expected latent period of latent fox
#infectious.period = expected life span of infected fox
#percent = % of N that must be Removed for time-step to be returned 
#percent.dead = number of foxes that must be Removed for time-step to be returned
#vacc = random sample of foxes assigned to be vaccinated foxes

#MATRICES - PERMANENT WITHIN EACH RUN
#overlap.area = area of overlap between foxes i and j (N x N)
#minta = minta value for foxes i and j (N x N)
#B = infection probablity = contact*transmission.probability
#status = status of all foxes from time t=0 to t=time (N x time)

#VARIABLES - TEMPORARY (MOSTLY IN LOOPS)
#need.new = do we need to sample a new xy?
#trial = limit of attempts to sample new fox
#reject = for weighting y sampling
#keep = for weighting y sampling
#minta.too.big = is minta < 0.75?
#d = distance between home range centers
#r = minimum radius
#R = maximum radius
#theta1 = angle of smaller circle
#theta2 = angle of larger circle
#outside = area of small circle outside the larger circle when (R-r)<d && d<(r+R)
#contact = daily contact rate for foxes i and j (N x N)
#new = number of new latent animals per infectious fox at each time-step
#i = fox in loop
#j = fox in loop
#s = simulation loop
#t = time loop
#infectives = infectious neighbor foxes
#firewall = y value chosen to be center of vaccination firewall
#firewall.distance = distance between every y value and the firewall
#possible.vacc = the fox numbers for each firewall.distance
#firewall.foxes = matrix of firewall.distance and possible.vacc ordered by firewall.distance

#FUNCTIONS
#generate.radius(y) = calls function "rnorm" to generate a radius for a fox home range according to the fox' y value
#distance(x1,y1,x2,y2) = calculates the distance between two xy values
#daily.contact.rate = calls function "range" to generate a daily contact rate for two foxes i and j according to minta ij
#habitat.function = determine habitat type of fox home range based on y coordinate
#reject.function = for weighting y sampling

#OUTPUT VARIABLES AFTER ALL SIMULATIONS
#summary.N
#summary.density
#summary.seed
#summary.status.totals.at.end
#summary.Ro
#summary.spread
#summary.time.at.percent.dead
#summary.infectious.at.percent.dead
#summary.latent.at.percent.dead
#percent.S.mean = mean percent of original suceptible population still Suceptible at (t=365 averaged over all simulations)
#percent.L.mean = mean percent of original suceptible population still Latent at (t=365 averaged over all simulations)
#percent.I.mean = mean percent of original suceptible population still Infectious at (t=365 averaged over all simulations) 
#percent.R.mean = mean percent of original suceptible population still Removed at (t=365 averaged over all simulations)
#epidemic.fadeouts = number of simulations with epidemic fadeout 
#fox.extinctions = number of simulations with fox extinction 
#average.Ro = mean number of secondary infections caused by seed fox, averaged over all simulations
#Re.time = number of secondary infections caused by each infectious fox, averaged over each day, and each simulation
#Re.individuals = number of latent animals (N-S)/number of infectious animal days

#################################################################################
########################### SETUP ENVIRONMENT ##################################
################################################################################

##
## Set permanent variables
##
#Set number of runs
sim<-100
#Set number of time-steps
time<-365
#Population size
target.N<-2000
#Set island dimensions
X<-5000
Y<-30000
#Number of simulations to run between resampling home ranges
resample.N<-seq(from=1,to=sim,by=10)
#Probability of infection given contact between Susceptible and Infectious fox
transmission.probability<-0.49
#Average latent period of 42 days, mortality rate = 1/42  
latent.period<-1/42
#Cut off for latent period when fox is forced into Infectious class
latent.cut.off<-90
#Average life span of 4 days for infectious period, mortality rate = 1/4
infectious.period<-1/4
#Cut off for infectious period when fox is forced into Removed class
infectious.cut.off<-14
#% of N dead for record of time at % dead
percent<-0.5

##
## Create summary vectors for data across all simulations
## 
#Population size
summary.N<-c()
rownames(summary.N)<-rownames(summary.N,prefix="sim.")
#Densities
summary.density<-matrix(data=NA,nrow=4,ncol=sim)
rownames(summary.density)<-c("dunes","MDS.rugged","MDS.gentle","grass")
colnames(summary.density)<-colnames(summary.density,do.NULL=FALSE,prefix="sim.")
#Seed location
summary.seed<-matrix(data=NA,nrow=sim,ncol=2)
rownames(summary.seed)<-rownames(summary.seed,prefix="sim.")
colnames(summary.seed)<-c("x coord.","y coord.")
#total.0 = number of susceptible foxes at each time step in each simulation
summary.total.0<-matrix(data=NA,nrow=time,ncol=sim)
rownames(summary.total.0)<-rownames(summary.total.0,do.NULL=FALSE,prefix="t.")
colnames(summary.total.0)<-colnames(summary.total.0,do.NULL=FALSE,prefix="sim.")
#total.1 = number of latent foxes at each time step in each simulation
summary.total.1<-matrix(data=NA,nrow=time,ncol=sim)
rownames(summary.total.1)<-rownames(summary.total.1,do.NULL=FALSE,prefix="t.")
colnames(summary.total.1)<-colnames(summary.total.1,do.NULL=FALSE,prefix="sim.")
#total.2 = number of infectious foxes at each time step in each simulation
summary.total.2<-matrix(data=NA,nrow=time,ncol=sim)
rownames(summary.total.2)<-rownames(summary.total.2,do.NULL=FALSE,prefix="t.")
colnames(summary.total.2)<-colnames(summary.total.2,do.NULL=FALSE,prefix="sim.")
#total.3 = number of removed foxes at each time step in each simulation
summary.total.3<-matrix(data=NA,nrow=time,ncol=sim)
rownames(summary.total.3)<-rownames(summary.total.3,do.NULL=FALSE,prefix="t.")
colnames(summary.total.3)<-colnames(summary.total.3,do.NULL=FALSE,prefix="sim.")
#total.4 = number of vaccinated foxes at each time step in each simulation
summary.total.4<-matrix(data=NA,nrow=time,ncol=sim)
rownames(summary.total.4)<-rownames(summary.total.4,do.NULL=FALSE,prefix="t.")
colnames(summary.total.4)<-colnames(summary.total.4,do.NULL=FALSE,prefix="sim.")
#status.totals.at.end = sum of all foxes in each disease class at last time-step
summary.status.totals.at.end<-matrix(data=NA,nrow=5,ncol=sim)
rownames(summary.status.totals.at.end)<-c("total.0","total.1","total.2","total.3","total.4")
colnames(summary.status.totals.at.end)<-colnames(summary.status.totals.at.end,do.NULL=FALSE,prefix="sim.")
#Ro = Ro for seed fox
Ro<-rep(0,sim)
summary.Ro<-c()
rownames(summary.Ro)<-rownames(summary.Ro,prefix="sim.")
#Re = Re for entire epidemic
Re.time<-c()
summary.Re<-rep(0,sim)
#spread = distance between seed fox and furthest infected fox (I or L) at each time-step
summary.spread<-matrix(data=NA,nrow=time,ncol=sim)
rownames(summary.spread)<-rownames(summary.spread,do.NULL=FALSE,prefix="t.")
colnames(summary.spread)<-colnames(summary.spread,do.NULL=FALSE,prefix="sim.")
#time.at.percent.dead = time-step at which ___% of N are Removed
summary.time.at.percent.dead<-c()
rownames(summary.time.at.percent.dead)<-rownames(summary.time.at.percent.dead,prefix="sim.")
#infectious.at.percent.dead = number of foxes Infectious in time-step at which ___% of N are Removed
summary.infectious.at.percent.dead<-c()
rownames(summary.infectious.at.percent.dead)<-rownames(summary.infectious.at.percent.dead,prefix="sim.")
#latent.at.percent.dead = number of foxes Latent in time-step at which ___% of N are Removed   
summary.latent.at.percent.dead<-c()
rownames(summary.latent.at.percent.dead)<-rownames(summary.latent.at.percent.dead,prefix="sim.")

##
## FUNCTIONS
##
#Function to calculate distance between two fox home range centers
distance<-function(x1,y1,x2,y2) {sqrt((x2-x1)^2+(y2-y1)^2)}
#Function to generate radius for each fox depending on where the y value is 
#(creates a gradient of small to large home range sizes)
generate.radius<-function(y){
if (y<=(0.30*Y))  r<-rnorm(n=1,mean=6.570392,sd=0.2348970) #Grass
else 
if ((0.30*Y)<y && y<=(0.60*Y)) r<-rnorm(n=1,mean=5.642243,sd=0.2214349) #MDS.Rugged
else 
if ((0.60*Y)<y && y<=(0.90*Y)) r<-rnorm(n=1,mean=6.223819,sd=0.3502707) #MDS.Gentle
else  r<-rnorm(n=1,mean=5.530671,sd=0.4102617) #Dunes
exp(r)
}
#Reject function
reject.function<-function(y){
if (y<=(0.30*Y))  0.21 #Grass
else 
if ((0.30*Y)<y && y<=(0.6*Y)) 0.77 #MDS.Rugged
else 
if ((0.6*Y)<y && y<=(0.90*Y)) 0.28 #MDS.Gentle
else  1 #Dunes  
}
#Assign habitat type
habitat.function<-function(y){
if (y<=(0.30*Y))  "grass"
else 
if ((0.30*Y)<y && y<=(0.6*Y)) "MDS.rugged"
else 
if ((0.6*Y)<y && y<=(0.90*Y)) "MDS.gentle"
else  "dunes" 
}
#Function for per day contact rate based on minta
daily.contact.rate<-function(m){
#if overlap is zero, there is no contact
if (m==0) sample<-0 else{
#equation for lm(merged.contacts.per.day.number~FK.95.Hpi_minta.overlap.index,data=prox.pairs.short)
average=0.02164+(0.87752*m) 
#equation for lm((linear$residuals^2)~FK.95.Hpi_minta.overlap.index,data=prox.pairs.short) with intercept fixed at 0
variance=0+(0.245243*m)
sample<-rnorm(n=1,mean=average,sd=sqrt(variance))
if (sample<0) sample<-0
}
sample
} 

################################################################################
############################ START SIMULATION ##################################
################################################################################

for (s in 1:sim){

########## Create Home Ranges and Overlap/Minta/Transmission Matrices  #########

if (sum(s==resample.N)>0){
##
## Re-set all variables at start of each simulation
##
#Set fox population size
N<-target.N
fox<-c()
x<-c()
y<-c()
radius<-c()
HR.area<-c()
habitat<-c()
overlap.area<-matrix(data=NA,nrow=N,ncol=N)
minta<-matrix(data=NA,nrow=N,ncol=N)
B<-matrix(data=NA,nrow=N,ncol=N)
new.latents<-c()
fox.home.ranges<-c()
 
#Select first home range
fox<-1
x[1]<-sample(0:X,1)
y[1]<-sample(0:Y,1)
radius[1]<-generate.radius(y[1])
HR.area[1]<-pi*(radius[1]^2)
habitat[1]<-habitat.function(y[1])

#Loop to create home ranges one by one, checking the distance btwn them as you go.
for (i in 2:N)
{
#Fill vectors for x,y,r
need.new<-1
trial<-0
fox[i]<-i
while (need.new==1) 
{
x[i]<-sample(0:X,1)
y[i]<-sample(0:Y,1)
reject<-reject.function(y[i])
keep<-(sample(0:100,1)/100)
while (keep>=reject){
x[i]<-sample(0:X,1)
y[i]<-sample(0:Y,1)
reject<-reject.function(y[i])
keep<-(sample(0:100,1)/100)
} #end while statement on keep<reject
radius[i]<-generate.radius(y[i])
HR.area[i]<-pi*(radius[i]^2)
habitat[i]<-habitat.function(y[i])
trial<-trial+1
minta.too.big<-0

for (j in 1:(i-1)){
d<-distance(x[i],y[i],x[j],y[j])
r<-min(radius[i],radius[j]) 
R<-max(radius[i],radius[j])

#If the smaller circle is completely inside the larger, overlap = the area of the smaller circle
if (r<=(R-d)) overlap.area[i,j]<-min(HR.area[i],HR.area[j])
else
#If there is no overlap, overlap = 0
if (d>=(r+R)) overlap.area[i,j]<-0 
else
#If the smaller circle is >0.5 inside the larger, calculate the area
if ((R-r)<d && d<(r+R)){
#Area of segment of circle 1
theta1<-acos(((d^2)+(r^2)-(R^2))/(2*d*r)) 
#Area of segment of circle 2
theta2<-acos(((d^2)-(r^2)+(R^2))/(2*d*R))
#"overlap" of small circle - "overlap" of large circle = area of small circle outside the big circle  
outside<-(0.5*(r^2)*(theta1-sin(theta1)))-(0.5*(R^2)*(theta2-sin(theta2))) 
#Area of overlap between two circles
overlap.area[i,j]<-min(HR.area[i],HR.area[j])-outside 
} else{
#If the smaller circle is <0.5 inside the larger, calculate the area
#Area of segment of circle 1
theta1<-acos(((d^2)+(r^2)-(R^2))/(2*d*r)) 
#Area of segment of circle 2
theta2<-acos(((d^2)-(r^2)+(R^2))/(2*d*R))
#Segment 1 + segment 2 - two triangles
overlap.area[i,j]<-(0.5*(r^2)*(theta1-sin(theta1)))+(0.5*(R^2)*(theta2-sin(theta2)))
} #End if statement to calculate overlap

#Calculate minta 
minta[i,j]<-sqrt((overlap.area[i,j]/HR.area[i])*(overlap.area[i,j]/HR.area[j]))
if (minta[i,j]>0.75){
#exit the j loop once we have one distance greater than threshold
minta.too.big<-1
break
} else{
#Assign value to other half of minta matrix
minta[j,i]<-minta[i,j]
#Assign value to transmission matrix. (contact*probability of infection)
B[i,j]<-(daily.contact.rate(minta[i,j])*transmission.probability)
if (B[i,j]>1) B[i,j]<-1
if (B[i,j]<0) B[i,j]<-0
B[j,i]<-B[i,j]
} #End else statment on minta check
} #End j loop

#If none of the mintas were too big, and no centers are the same, we don't need to re-sample a new location
if (minta.too.big==0) need.new<-0 
#If trial = 400, island is full and we don't need a new location
if (trial==400) break  
} #end of while statement
if (trial==400) break
} #end of i loop    

#Update vectors/matrices according to new N value
if (trial==400) {
fox<-fox[1:(length(x)-1)]
x<-x[1:(length(x)-1)]
y<-y[1:(length(y)-1)]
radius<-radius[1:(length(radius)-1)] 
HR.area<-HR.area[1:(length(HR.area)-1)]
habitat<-habitat[1:(length(habitat)-1)]
overlap.area<-overlap.area[1:(length(fox)),1:(length(fox))]
minta<-minta[1:(length(fox)),1:(length(fox))]
B<-B[1:(length(fox)),1:(length(fox))]
} 
N<-length(fox)
percent.dead<-round(percent*N)

#Update end population matrix
summary.N[s:(s+9)]<-N

#Update summary.density matrix
summary.density[1,s:(s+9)]<-sum(habitat=="dunes")/(0.1*X*Y/1000000)  
summary.density[2,s:(s+9)]<-sum(habitat=="MDS.rugged")/(0.3*X*Y/1000000)
summary.density[3,s:(s+9)]<-sum(habitat=="MDS.gentle")/(0.3*X*Y/1000000)
summary.density[4,s:(s+9)]<-sum(habitat=="grass")/(0.3*X*Y/1000000)

} #End of if statement to resample foxes and home ranges

####################### Seed Disease and Loop Time #############################

#Disease classes:
#Susceptible = 0
#Latent = 1
#Infectious = 2
#Removed = 3
#Vaccinated = 4

#Create empty matrix of dimensions N by T
status<-matrix(nrow=N,ncol=time)
#All foxes susceptible at time = 1
status[,1]<-0
#Vaccinate foxes - not done in this version of the model

#Seed disease at max or min y value
# Use maximum value for high density introduction = potential.seeds<-c(which(y==max(y)),which(y>(Y-300)))
# Use minimum value for low density introduction = potential.seeds<-c(which(y==min(y)),which(y<300))
potential.seeds<-c(which(y==max(y)),which(y>(Y-300)))
if (length(potential.seeds)==1) seed<-potential.seeds else seed<-sample(potential.seeds,1)
status[seed,1]<-2

new.latents<-c()
new.latents[1]<-0
#Loop time
for (t in 2:time)
{
new.latents[t]<-0
for (i in 1:N)
{
#If a fox is Removed
if (status[i,(t-1)]==3) status[i,t]<-3 
else
#If a fox is Vaccinated
if (status[i,(t-1)]==4) status[i,t]<-4  
else 
#If a fox is Latent
if (status[i,(t-1)]==1) {
#Average latent period of 42 days, mortality rate = 1/42, cut off at 90 days
if (t==(latent.cut.off+1) && status[i,(t-latent.cut.off)]==1) status[i,t]<-2 else {if (runif(1,min=0,max=1)<=(latent.period)) status[i,t]<-2 
else{
status[i,t]<-1} 
} 
} #End if statement on latent fox i 
else
#If a fox is Infectious
if (status[i,(t-1)]==2) {  
#Average life span of 4 days, mortality rate = 1/4, cut off at 14 days
if (t==(infectious.cut.off+1) && status[i,(t-infectious.cut.off)]==2) status[i,t]<-3 else{ if (runif(1,min=0,max=1)<=(infectious.period)) status[i,t]<-3
else{
status[i,t]<-2
if (i==seed) Ro[s]<-Ro[s]+1}
}
} #End if statement for infectious fox i
else 
#If a fox is Susceptible, check the status of it's neighbors
if (status[i,(t-1)]==0){
#Which foxes are infectious at time t-1?
infectives<-which(status[,t-1]==2)  
random.sample<-runif(length(infectives),min=0,max=1)
#Infection occurs through contact with neighbors or background transmission rate
if (sum(random.sample<=B[i,infectives],na.rm=TRUE)>0 | runif(1,min=0,max=1)<(1-(1-0.000001)^length(infectives))){
status[i,t]<-1 
new.latents[t]<-new.latents[t]+1
} #End if statement on infection 
else status[i,t]<-0
} #End of if statement on susceptible fox i
} #End i loop
} #End t loop
                      
####################### Calculate Output Variables #############################

##
##Population size
##
summary.N[s]<-N

##
##Seed location
##
summary.seed[s,1]<-x[seed]
summary.seed[s,2]<-y[seed]

##
##Number of foxes in each stage at each time step
##
total.0<-colSums(status==0,na.rm=FALSE,dims=1)
total.1<-colSums(status==1,na.rm=FALSE,dims=1)
total.2<-colSums(status==2,na.rm=FALSE,dims=1)
total.3<-colSums(status==3,na.rm=FALSE,dims=1)
total.4<-colSums(status==4,na.rm=FALSE,dims=1)

#total.0 = number of latent foxes at each time step in each simulation
summary.total.0[,s]<-total.0
total.0.means<-apply(summary.total.0,1,mean)
#total.1 = number of latent foxes at each time step in each simulation
summary.total.1[,s]<-total.1
total.1.means<-apply(summary.total.1,1,mean)
#total.2 = number of infectious foxes at each time step in each simulation
summary.total.2[,s]<-total.2
total.2.means<-apply(summary.total.2,1,mean)
#total.3 = number of removed foxes at each time step in each simulation
summary.total.3[,s]<-total.3
total.3.means<-apply(summary.total.3,1,mean)
#total.4 = number of vaccinated foxes at each time step in each simulation
summary.total.4[,s]<-total.4
total.4.means<-apply(summary.total.4,1,mean)
#total.i = number of infected foxes at each time step in each simulation
summary.total.i<-summary.total.1+summary.total.2
total.i.means<-apply(summary.total.i,1,mean)

##
##Number of foxes in each stage at the end of every simulation
##
status.totals.at.end<-rbind(total.0,total.1,total.2,total.3,total.4)
summary.status.totals.at.end[,s]<-status.totals.at.end[,time]

##
##Re.time
##

Rs<-c()
Re.time<-c()
for (t in 2:time)
{
new<-(new.latents[t]/total.2[t-1])
if (new=="-Inf" | new=="Inf" | new=="NA" | new=="NaN" | new<0) Rs[t]<-0 
else Rs[t]<-new
}
summary.Re[s]<-mean(Rs,na.rm=TRUE)
Re.time<-mean(summary.Re)

##
##Calculate distance of spread after each day
##
spread<-c()
for (t in 1:time)
{
if (t==1) spread[t]<-0
else{
d<-c()
for (i in 1:N)
{
if (i==seed) d[i]<-0
if (status[i,t]==0 | status[i,t]==4 ) next
else{
#Distace between home range centers
d[i]<-distance(x[seed],y[seed],x[i],y[i])
} #End else statement
} #End i loop
spread[t]<-max(d,na.rm=TRUE)
} #End if statement
} #End t loop
summary.spread[,s]<-spread

##
##Calculate how many time-steps until a certain % of foxes are dead, and the # Infectious and Latent foxes at that time-step
##
if (length(which(total.3>=percent.dead)>0)){
summary.time.at.percent.dead[s]<-min(which(total.3>=percent.dead))
summary.infectious.at.percent.dead[s]<-total.2[summary.time.at.percent.dead[s]]
summary.latent.at.percent.dead[s]<-total.1[summary.time.at.percent.dead[s]]
} else {
summary.time.at.percent.dead[s]<-NA
summary.infectious.at.percent.dead[s]<-NA
summary.latent.at.percent.dead[s]<-NA
} #End else statment

} #End sim loop

##
## Percent of original S in each status class at t=365
##

#Percent Suceptible at t=365
percent.S.mean<-mean((summary.total.0[365,]/(summary.N-summary.total.4[1,])))

#Percent Latent at t=365
percent.L.mean<-mean((summary.total.1[365,]/(summary.N-summary.total.4[1,])))

#Percent Infectious at t=365
percent.I.mean<-mean((summary.total.2[365,]/(summary.N-summary.total.4[1,])))

#Percent Removed at t=365
percent.R.mean<-mean((summary.total.3[365,]/(summary.N-summary.total.4[1,])))

##
## Number of simulations with epidemic fadeout 
##
epidemic.fadeouts<-sum(summary.status.totals.at.end[1,]>0 & summary.status.totals.at.end[2,]==0 & summary.status.totals.at.end[3,]==0,na.rm=TRUE)

##
##Number of simulations with fox extinction 
##
fox.extinctions<-sum(summary.status.totals.at.end[4,]==(summary.N-summary.total.4[1,]))

##
##Percent Suceptible at t=average.detection.day
##
percent.S.at.average.detection.day<-mean(summary.total.0[average.detection.day,]/(summary.N-summary.total.4[1,]))

#Percent Latent at t=average.detection.day
percent.L.at.average.detection.day<-mean(summary.total.1[average.detection.day,]/(summary.N-summary.total.4[1,]))


##
##Ro
##

average.Ro<-mean(Ro)

##
##Re.individuals
##

Re.individuals<-mean(((summary.N-summary.total.4[1,])-summary.total.0[365,])/colSums(summary.total.2))


#Save all objects with a detailed file name
save(list=ls(all=TRUE),file="SCI_Rabies_VaccNone_IntroHigh_Main.RData")

################################################################################
############################## END SIMULATION ##################################
################################################################################

rm(list=ls(all=TRUE))