2019nCov_model_determ_with quarantine_2.0_20200318.R

rm(list = ls())

#title: "Deterministic compartmental model for 2019-nCov 2.0 "
#author: "Antoinette Ludwig, Erin Rees'

#date: "March, 16th, 2020"

#################################################################################################

### Resources:

#http://sherrytowers.com/2015/10/01/difference-between-markov-chain-monte-carlo-stochastic-differential-equations-and-agent-based-models/
#http://sherrytowers.com/2016/02/06/stochastic-compartmental-modelling-with-stochastic-differential-equations-2/
#https://cran.r-project.org/web/packages/MultiBD/vignettes/SIR-MCMC.pdf
#https://cran.r-project.org/web/packages/GillespieSSA/index.html
#https://math.unm.edu/~sulsky/mathcamp/SimpleStochModel.pdf


# Gillispie method for random noise added to demographics
# Includes stochasticity for the timing of the next event, and which event is next
# Continuous time, discrete population changes

# But instead, this approach adds stochasticity via the mechanistic parameters (e.g. contact rate)

#################################################################################################

# install.packages('deSolve')
# install.packages('ggplot2')
# install.packages('tidyr')
# install.packages('dplyr')
# install.packages('tidyverse')
# install.packages('matrixStats')
#install.packages('xlsx')
#install.packages('triangle')
### Libinstall.packages()

library(deSolve)
library(ggplot2)
library(tidyr)
library(dplyr)
library(tidyverse)
library(matrixStats)
#library(xlsx)
#library(triangle)
#require(GillespieSSA)

#################################################################################################

### User input for the initial conditions

N <- 1000000 # Total population for the simulation: large sized city
inputL <- 100 # initial exposed
inputL_q <- 0  # initial exposed quarantined
inputL_r <- 0  # initial exposed refractory to social dstancing
inputI_a <- 100 # initial pre-symptomatic for non symptomatic
inputI_ar <- 0 # initial pre-symptomatic for refractory to social dstancing
inputI_aq <- 0 # initial pre-symptomatic for non symptomatic in quarantine and complient with quarantine
inputI_aqn <- 0 # initial pre-symptomatic for non symptomatic in quarantine and not complient with quarantine
inputI_sm <- 0 # initial symptomatic until testing with mild symptoms 
inputI_ss <- 0 # initial symptomatic until testing with severe symptoms
inputI_smr <- 0 # initial symptomatic until testing with mild symptoms refractory to social distancing
inputI_ssr <- 0 # initial symptomatic until testing with severe symptoms refractory to social distancing
inputI_smis <- 0 # initial symptomatic isolated with mild symptoms
inputI_smisn <- 0 # initial symptomatic not isolated with mild symptoms
inputI_ssis <- 0 # initial symptomatic isolated with severe symptoms
inputI_ssisn <- 0 # initial symptomatic not isolated with severe symptoms
inputI_ssh <- 0 # initial symptomatic hospitalized with severe symptoms

inputI_smrisn <- 0 # initial symptomatic not isolated with mild symptoms refractory to social distancing
inputI_ssrisn <- 0 # initial symptomatic not isolated with severe symptoms refractory to social distancing

inputI_smqisn <- 0 # initial symptomatic not isolated with mild symptoms coming from quarantine

inputR  <- 0 # initial recovered population
inputD <- 0 #initial death population


# Number of times to run the simulation

nSim <- 1

#################################################################################################


### Function with the differential equations

# S = susceptible
# L = latent(incubant)
# L_q = latent (incubant) in quarantine
# L_r = latent (icubant) refractory to social distancing
# I_a = pre-symptomatic infectious
# I_ar = pre-symptomatic infectious refractory to social distancing
# I_aq = pre-symptomatic infectious in quarantine and complient
# I_aqn = pre-symptomatic infectious in quarantine and not complient
# I_sm = symptomtic with mild symptoms before diagnostic
# I_ss = symptomatic with severe symptoms before diagnostic
# I_smr = initial symptomatic until testing with mild symptoms refractory to social distancing
# I_ssr = initial symptomatic until testing with severe symptoms refractory to social distancing
# I_smis = symptomatic with mild symptoms after diagnostic in isolation
# I_smisn = symptomatic with mild symptoms after diagnostic not in isolation
# I_ssis = symptomatic with severe symptoms after diagnostic in isolation
# I_ssisn = symptomatic with severe symptoms after diagnostic not in isolation
# I_ssh =  symptomatic with severe symptoms after diagnostc hospitalized
# I_smrisn = initial symptomatic not isolated with mild symptoms refractory to social distancing
# I_ssrisn = initial symptomatic not isolated with severe symptoms refractory to social distancing
# I_smqisn = symptomatic in quarantine with mild symptoms who don't continue in isolation
# 
# R = recovered
# D= Dead from infection 



#Density dependent contact rate formulation


seir <- function(time, state, parms) {
  
  with(as.list(c(state, parms)), {
    
    #dS <- -beta*c*(1-lambda)*tau*S*(I_a + I_aqn + I_sm + I_ss + I_smisn + I_ssisn) -beta*cr*(1-lambda)*(1-tau)*S*(I_ar+I_smr+I_ssr+I_smrisn+I_ssrisn)-beta*cq*lambda*S*I_aq
    dS <- -beta*((c*(1-lambda)*tau)+(cq*lambda)+(cr*(1-lambda)*(1-tau)))*S*(I_a + I_aqn + I_sm + I_ss + I_smisn + I_ssisn+I_ar+I_smr+I_ssr+I_smrisn+I_ssrisn+phi*I_aq)
    dL <- (1-lambda)*beta*c*tau*S*(I_a + I_aqn + I_sm + I_ss + I_smisn + I_ssisn+I_ar+I_smr+I_ssr+I_smrisn+I_ssrisn+phi*I_aq) - sigma*L
    dL_q <- lambda*beta*cq*S*(I_a + I_aqn + I_sm + I_ss + I_smisn + I_ssisn+I_ar+I_smr+I_ssr+I_smrisn+I_ssrisn+phi*I_aq) - sigma*L_q
    dL_r <-  beta*cr*(1-lambda)*(1-tau)*S*(I_a + I_aqn + I_sm + I_ss + I_smisn + I_ssisn+I_ar+I_smr+I_ssr+I_smrisn+I_ssrisn+phi*I_aq)-sigma*L_r
    dI_a <- sigma*L - I_a*delta*epsilon - I_a*(1-delta)*upsilon
    dI_aq <- sigma*rho*L_q - I_aq*delta*epsilon - I_aq*(1-delta)*upsilon
    dI_ar <- sigma*L_r - I_ar*delta*epsilon - I_ar*(1-delta)*upsilon
    dI_aqn <- sigma*(1-rho)*L_q - I_aqn*delta*epsilon - I_aqn*(1-delta)*upsilon
    dI_sm <- I_a*delta*epsilon*alpha - kappa*I_sm
    dI_ss <- I_a*delta*epsilon*(1-alpha) - kappa*I_ss
    dI_smr <- I_ar*delta*epsilon*alpha - kappa*I_smr
    dI_ssr <- I_ar*delta*epsilon*(1-alpha) - kappa*I_ssr
    dI_smis <- kappa*feim*I_sm + kappa*feimr*I_smr + delta*alpha*epsilonq*feimq*I_aq - num*I_smis
    dI_smisn <- kappa*(1-feim)*I_sm - num*I_smisn
    dI_ssis <- kappa*feisi*(I_ss+I_ssr) - I_ssis*((1-mu)*nus + mu*nud)
    dI_ssisn <- kappa*(1-feisi-feish)*(I_ss+I_ssr) - I_ssisn*((1-mu)*nus + mu*nud)
    dI_ssh <- kappa*feish*(I_ss+I_ssr) + delta*(1-alpha)*epsilonq*I_aq - I_ssh*((1-mu)*nus + mu*nud)
    dI_smrisn <- kappa*(1-feimr)*I_smr - num*I_smrisn
    dI_ssrisn <- kappa*(1-feisi-feish)*(I_ssr) - I_ssrisn*((1-mu)*nus + mu*nud)
    dI_smqisn <- I_aq*delta*alpha*epsilonq*(1-feimq) - num*I_smqisn
    
    dR <- (I_a +I_aq+I_aqn+I_ar)*(1-delta)*upsilon + num*(I_smis+I_smisn+I_smqisn+I_smrisn) + (I_ssis + I_ssisn + I_ssh+I_ssrisn)*(1-mu)*nus
    dD <- mu*nud*(I_ssis + I_ssisn + I_ssh + I_ssrisn)
    
    return(list(c(dS, dL, dL_q, dL_r, dI_a, dI_aq, dI_ar, dI_aqn, dI_sm, dI_ss,dI_smr, dI_ssr, dI_smis, dI_smisn, dI_ssis, dI_ssisn, dI_ssh, dI_smrisn, dI_ssrisn, dI_smqisn, dR, dD)))
  })
}

### Set time frame in days

t <- seq(0, 1500, by = 1)

### Set initial compartment states as proportions 

init <- c(S = N,
          L = inputL,
          L_q= inputL_q,
          L_r = inputL_r,
          I_a = inputI_a,
          I_aq = inputI_aq,
          I_ar = inputI_ar,
          I_aqn = inputI_aqn,
          I_sm = inputI_sm,
          I_ss = inputI_ss,
          I_smr = inputI_smr,
          I_ssr = inputI_ssr,
          I_smis = inputI_smis,
          I_smisn = inputI_smisn,
          I_ssis = inputI_ssis,
          I_ssisn = inputI_ssisn,
          I_ssh = inputI_ssh,
          I_smrisn = inputI_smrisn,
          I_ssrisn = inputI_ssrisn,
          I_smqisn = inputI_smqisn,
          R = inputR,
          D= inputD)

### Define the parameter values

# c = contact rate
# cr = contact rate for refractory people
# cq =  contact rate for quarantined people
# beta = transmission probability
# sigma = 1 / latency period
# lambda = proportion of exposed (incubant) individuals are detected and placed in quarantine (contact tracing)
# rho = quarantine complience rate
# epsilon = 1/pre-symptomatic infectious period
# epsilonq = 1/(pre-symptomatic infectious period +duration between onset of symptoms and diagnostic)
# alpha = percentage of infectious (symptomatic) that develop mild symptoms
# delta = percentage of infectious pre-symptomatic who will develop symptoms
# upsilon = 1/duration of the asymptomatic period between pre-symptomatic and recovery
# num = 1/duration of symptomatic period for mild cases before recover
# nus = 1/duration of symptomatic period for severe cases before recover
# nud = 1/duration of symptomatic period for severe cases before dying
# kappa =  1/duration between onset of symptoms and diagnostic
# feim = percentage of mild cases who go in isolation
# feisi =  percentage of severe cases who go in isolation
# feish = percentage of severe cases who go in hospital
# feimq = percentage of mild cases in quarantine who go in isolation
# feimr = percentage of mild cases refractory who go in isolation
# mu = percentage of severe cases dying
# tau = Tau = complience rate with social distancing measures
# phi = modulator (percentage) for the effect of quarantine infetious on transmission



#################################################################################################

# Simulation

# Create list to store model output
listOut <- NULL
listOut <- list()


for(i in seq(1, nSim, 1)){
  
  rand_c <- 8 #Béreaud paper Min=6 Max=11
  rand_cr <- 11
  rand_cq <- 4 # individual at home
  rand_beta <- 0.05/N # Stilianakis 2010 (Vicky's value=0.017)
  rand_sigma <- 1/3.7
  rand_lambda <- 0.5 # Min=0% Max=50%
  rand_rho <- 0.95 # Min=75% Max=95%
  rand_epsilon <- 1/2.5
  rand_epsilonq <- 1/4.5
  rand_alpha <- 0.56
  rand_delta <- 1-0.065 # to validate
  rand_upsilon <- 1/15 
  rand_num <- 1/12.5
  rand_nus <- 1/26
  rand_nud <- 1/26
  rand_kappa <- 1/2
  rand_feim <-  1 #Max=100% Min =80%
  rand_feisi <- 0 # feish + feisi must be below 1
  rand_feish <- 1 # feish + feisi must be below 1
  rand_feimq <- 1 #Max=100% Min=80%
  rand_feimr <- 0.9 #Max=90% Min=80%
  rand_mu <- 0.12
  rand_tau <- 0.6 #Min=60% Max=90%
  rand_phi <- 0
  

  params <- c(c = rand_c,
              cr = rand_cr,
              cq = rand_cq,
              beta = rand_beta,
              sigma = rand_sigma,
              lambda = rand_lambda,
              rho = rand_rho,
              epsilon = rand_epsilon,
              epsilonq = rand_epsilonq,
              alpha = rand_alpha,
              delta = rand_delta,
              upsilon = rand_upsilon,
              num = rand_num,
              nus = rand_nus,
              nud = rand_nud,
              kappa = rand_kappa,
              feim = rand_feim,
              feimr= rand_feimr,
              feisi = rand_feisi,
              feish = rand_feish,
              feimq = rand_feimq,
              mu = rand_mu,
              tau = rand_tau,
              phi = rand_phi) 
  
  ### Run the model
  
  out <- ode(y = init, times = t, func = seir, parms = params)
  
  # Add model output to list
  listOut[[i]] <- out
  
}


#################################################################################################

# Plot the results


## Plot


plotdata <- data.frame(x=t, y=out)

matplot(x = plotdata[,c("y.time")], y = plotdata[,c("y.S","y.L","y.L_q","y.I_a","y.I_aq","y.I_smis","y.I_ssh","y.R",'y.D')], type = "l",
        xlab = "Time", ylab = "individuals", main = "SEIR Model 2.0",
        lwd = 1, lty = 1, bty = "l", col = 2:11)

legend(250, 1000000, c("Susceptible", "Latent","Latent_q",  "Pre-sympt", 'Pre-sympto in quarantine','Symptomatic mild isolated','Symptomatic severe hospitalized','Recovered','Dead'), pch = 1, col = 2:11, bty = "n")



###################################################################################
##Calculate ouputs#######################
#############################################



  ### Number of infected over time
  ################################

plotdata$Infect <- plotdata$y.I_a+plotdata$y.I_aq+plotdata$y.I_ar + plotdata$y.I_aqn+plotdata$y.I_sm+plotdata$y.I_ss+plotdata$y.I_smis+plotdata$y.I_smr + plotdata$y.I_ssr + plotdata$y.I_smisn+plotdata$y.I_ssis+plotdata$y.I_ssisn+plotdata$y.I_ssh+ plotdata$y.I_smqisn+plotdata$y.I_smrisn+plotdata$y.I_ssrisn

matplot(x = plotdata[,c("y.time")], y = plotdata[,c('Infect')], type = "l",
        xlab = "Time", ylab = "individuals", main = "Infected",
        lwd = 2, lty = 1, bty = "l", col = 2)

#legend(250, 460000, c("Infected"), pch = 1, col = 2, bty = "n")

  # Max number of cases and date of peak
maxInfect<-max(plotdata$Infect)
maxInfect
datemaxInfect<-plotdata$y.time[plotdata$Infect==max(plotdata$Infect)]
datemaxInfect



  ### Number of new cases each day, over time (incidence)
  #######################################################

n<-nrow(plotdata)

#Calculate the incidence



plotdata$IncI <-NA
plotdata$IncI[1]<-plotdata$Infect[1]
for(i in 2:n)
  plotdata$IncI[i] <- ((plotdata$y.L[i-1]+plotdata$y.L_q[i-1]+plotdata$y.L_r[i-1]) * rand_sigma ) 


#Calculate the incidence max and the related date
maxInc<-max(plotdata$IncI)
maxInc
datemaxInc<-plotdata$y.time[plotdata$IncI==max(plotdata$IncI)]
datemaxInc

# Total number of cases
sumInfect<-sum(plotdata$IncI)
sumInfect

# Outbreak duration (when no new cases)

plotdata$cumI<-NA
plotdata$cumI[1]<-plotdata$IncI[1]
for(i in 2:n)
  plotdata$cumI[i] <- (plotdata$IncI[i] +plotdata$cumI[i-1]) 

matplot(x = plotdata[,c("y.time")], y = plotdata[,c('cumI')], type = "l",
        xlab = "Time", ylab = "individuals", main = "Cumulative incidence",
        lwd = 2, lty = 1, bty = "l", col = 6)

datemaxCumI<-plotdata$y.time[plotdata$cumI==max(plotdata$cumI)]
min(datemaxCumI)

# Attack rate
AR <- sumInfect*100/N
AR



### Hospitalized

plotdata$Hosp <- plotdata$y.I_ssh
matplot(x = plotdata[,c("y.time")], y = plotdata[,c('Hosp')], type = "l",
       xlab = "Time", ylab = "individuals", main = "Hospitalized",
       lwd = 2, lty = 1, bty = "l", col = 3)

#legend(250, 1000000, c("Hospitalized"), pch = 1, col = 3, bty = "n")


maxHosp<-max(plotdata$Hosp)
maxHosp
datemaxHosp<-plotdata$y.time[plotdata$Hosp==max(plotdata$Hosp)]
datemaxHosp

#### Quarantined

plotdata$Quarant <- plotdata$y.I_aq

matplot(x = plotdata[,c("y.time")], y = plotdata[,c('Quarant')], type = "l",
        xlab = "Time", ylab = "individuals", main = "Quarantined",
        lwd = 2, lty = 1, bty = "l", col = 4)

#legend(250, 1000000, c("Hospitalized"), pch = 1, col = 3, bty = "n")


maxQuarant<-max(plotdata$Quarant)
maxQuarant
datemaxQuarant<-plotdata$y.time[plotdata$Quarant==max(plotdata$Quarant)]
datemaxQuarant

 
##### Isolated
plotdata$Isolat <- plotdata$y.I_smis + plotdata$y.I_ssis

matplot(x = plotdata[,c("y.time")], y = plotdata[,c('Isolat')], type = "l",
        xlab = "Time", ylab = "individuals", main = "Isolated",
        lwd = 2, lty = 1, bty = "l", col = 5)


maxIsolat<-max(plotdata$Isolat)
maxIsolat
datemaxIsolat<-plotdata$y.time[plotdata$Isolat==max(plotdata$Isolat)]
datemaxIsolat
















##################################################################################################

#### Calculate R0 or Rt Reproductive number

# dI <- sigma*rho*L - (delta_I*(1-omega) +  gamma_I*omega)*I + mu*epsilon*A
# dA <- sigma*(1 - rho)*L - (1-epsilon)*gamma_A*A - mu*epsilon*A
###################################################################################################
epsilon  <-params['epsilon']
omega  <-params['omega']
plotdata <- data.frame(x=t, y=out)
n<-nrow(plotdata)

plotdata$Rt <-NA
plotdata$Rt[1]<-plotdata$y.I[1]
for(i in 2:n)
  plotdata$Rt[i] <- (plotdata$y.L[i-1]*rand_sigma*rand_rho -(rand_delta_I*(1-omega)+rand_gamma_I*omega)*plotdata$y.I[i-1]+plotdata$y.L[i-1]*rand_sigma*(1-rand_rho)-rand_gamma_A*(1-epsilon)*plotdata$y.A[i-1])

matplot(x = plotdata[,c("y.time")], y = plotdata[,c("Rt")], type = "l",
        xlab = "Time", ylab = "Rt", main = "Rt",
        lwd = 1, lty = 1, bty = "l", col = 2:11)

###################################################################
### for modelling report March 3rd 2020############################
###################################################################

# number of cases

  #Calculate the max number of cases

maxIinf <-max(plotdata$y.I)
maxIinf
  #Plot the number of cases

matplot(x = plotdata[,c("y.time")], y = plotdata[,c("y.I")], type = "l",
        xlab = "Time", ylab = "individuals", main = "Number of cases",
        lwd = 2, lty = 1, bty = "l", col = 2)


#Incidence
  
#Calculate the incidence
epsilon  <-params['epsilon']
plotdata <- data.frame(x=t, y=out)
n<-nrow(plotdata)

plotdata$IncI <-NA
plotdata$IncI[1]<-plotdata$y.I[1]
for(i in 2:n)
  plotdata$IncI[i] <- (plotdata$y.L[i-1]*rand_sigma*rand_rho + rand_mu*epsilon*plotdata$y.A[i-1]) 

  #Calculate the incidence max and the related date
maxInc<-max(plotdata$IncI)
maxInc
datemaxInc<-plotdata$y.time[plotdata$IncI==max(plotdata$IncI)]
datemaxInc



  #Plot the incidence

matplot(x = plotdata[,c("y.time")], y = plotdata[,c("IncI")], type = "l",
        xlab = "Time", ylab = "individuals", main = "Incidence",
        lwd = 2, lty = 1, bty = "l", col = 3)


#Cumulative incidence

plotdata$cumI<-NA
plotdata$cumI[1]<-plotdata$y.I[1]
for(i in 2:n)
  plotdata$cumI[i] <- (plotdata$y.L[i-1]*rand_sigma*rand_rho + rand_mu*epsilon*plotdata$y.A[i-1]+plotdata$cumI[i-1]) 

  #Calculate the max cumulative incidence and its related date (epidemic duration)
maxCumI<-max(plotdata$cumI)
maxCumI
datemaxCumI<-plotdata$y.time[plotdata$cumI==max(plotdata$cumI)]
min(datemaxCumI)

  #Plot the cumulative incidence

matplot(x = plotdata[,c("y.time")], y = plotdata[,c("cumI")], type = "l",
        xlab = "Time", ylab = "individuals", main = "Cumulative incidence",
        lwd = 2, lty = 1, bty = "l", col = 4)












###################################################################
# Validate the results with Wuhan data
###################################################################


#Comparison with First stages of the epidemic (Li, 2020)

setwd('D:/PED/Coronavirus/SEIR model/validation')
d<-read.table("WuhanForValidation.txt",header = T,fill=TRUE)


plotdata <- data.frame(x=t, y=out)


#New I cases at each time step
#dI <- sigma*rho*L - (delta_I*(1-omega) +  gamma_I*omega)*I + mu*epsilon*A
epsilon  <-params[3]

n<-nrow(plotdata)

plotdata <- data.frame(x=t, y=out)
plotdata$IncI <-NA
plotdata$IncI[1]<-plotdata$y.I[1]
for(i in 2:n)
  plotdata$IncI[i] <- (plotdata$y.L[i-1]*rand_sigma*rand_rho + rand_mu*epsilon*plotdata$y.A[i-1]) 


plotdata <-data.frame(plotdata$y.time,plotdata$IncI)
names(plotdata)[names(plotdata) == "plotdata.y.time"] <- "time"
names(plotdata)[names(plotdata) == "plotdata.IncI"] <- "IncI"


d2 <- data.frame(d)
plotdata2 <-merge (plotdata,d2, by='time', all = TRUE)

matplot(x = plotdata2[,c("time")], y = plotdata2[,c("IncI","casesL")], type = "l",
        xlab = "Time", ylab = "individuals", main = "Model comparison",
        lwd = 1, lty = 1, bty = "l", col = 2:11)

legend(250, 400000, c("Incidence rate of Inf","cases obs"), pch = 1, col = 2:11, bty = "n")

# zoon=m on the first 100 days

plotdata2zoom <-subset(plotdata2,plotdata2$time<45)

matplot(x = plotdata2zoom[,c("time")], y = plotdata2zoom[,c("IncI","casesL")], type = "l",
        xlab = "Time", ylab = "individuals", main = "Model comparison",
        lwd = 1, lty = 1, bty = "l", col = 2:11)












#plot for modeling report Feb27th 2020

datareport12 <- data.frame(x=t, y=out)#change the name of the dataset to reflect the value of the c parameter in the name
datareport12 <-data.frame(datareport12$y.time,datareport12$y.I,datareport12$y.A)
n<-nrow(datareport12)
datareport12$TotInf<-NA
for(i in 1:n)
  datareport12$TotInf[i] <- (datareport12$datareport12.y.I[i] + datareport12$datareport12.y.A[i]) 
names(datareport12)[names(datareport12) == "TotInf"] <- "TotInf12"
names(datareport12)[names(datareport12) == "datareport12.y.I"] <- "Inf12"
names(datareport12)[names(datareport12) == "datareport12.y.A"] <- "Asympt12"


datareport10 <- data.frame(x=t, y=out) 
n<-nrow(datareport10)
datareport10$TotInf<-NA
for(i in 1:n)
  datareport10$TotInf[i] <- (datareport10$y.I[i] + datareport10$y.A[i]) 


datareport8 <- data.frame(x=t, y=out) 
n<-nrow(datareport8)
datareport8$TotInf<-NA
for(i in 1:n)
  datareport8$TotInf[i] <- (datareport8$y.I[i] + datareport8$y.A[i]) 


datareport6 <- data.frame(x=t, y=out) 
n<-nrow(datareport6)
datareport6$TotInf<-NA
for(i in 1:n)
  datareport6$TotInf[i] <- (datareport6$y.I[i] + datareport6$y.A[i]) 

datareporttot <- merge(datareport10, datareport12, by='y.time') 
datareporttot <- merge(datareport8, datareporttot, by='y.time') 
datareporttot <- merge(datareport6, datareporttot, by='y.time') 

head(datareporttot)


matplot(x = datareporttot[,c("y.time")], y = datareporttot[,c("TotInf","TotInf.x","TotInf.y")], type = "l",
        xlab = "Time", ylab = "total number of infected", main = "Number of infected (asymptomatic and symptomatic)",
        lwd = 1, lty = 1, bty = "l", col = 2:11)

legend(450, 4000, c("contact rate=8","contact rate=10", "contact rate = 12"), pch = 1, col = 2:11, bty = "n")


######################### Output statistics

#Maximum number of cases
maxI<-max(plotdata$y.I)
maxI
datemaxI<-plotdata$y.time[plotdata$y.I==max(plotdata$y.I)]
datemaxI

maxA<-max(plotdata$y.A)
maxA
datemaxA<-plotdata$y.time[plotdata$y.A==max(plotdata$y.A)]
datemaxA

maxH<-max(plotdata$y.H)
maxH
datemaxH<-plotdata$y.time[plotdata$y.H==max(plotdata$y.H)]
datemaxH

maxR<-max(plotdata$y.R)
maxR

maxD<-max(plotdata$y.D)
maxD


# Cumulative number of infected non-infectious (A)
  # dA <- sigma*(1 - rho)*L - (1-epsilon)*gamma_A*A - mu*epsilon*A

n<-nrow(plotdata)

plotdata$cumA<-NA
plotdata$cumA[1]<-plotdata$y.A[1]
for(i in 2:n)
  plotdata$cumA[i] <- (plotdata$y.L[i-1]*rand_sigma*(1-rand_rho)) 
finalcumA <-sum(plotdata$cumA) #certainement inutil de faire une somme final: le dernier élémentd eligne devrait déjà donner le chiffre recherché


#Cumulative number of infected infectious (I)
  #dI <- sigma*rho*L - (delta_I*(1-omega) +  gamma_I*omega)*I + mu*epsilon*A
epsilon  <-params[3]
plotdata$cumI<-NA
plotdata$cumI[1]<-plotdata$y.I[1]
for(i in 2:n)
  plotdata$cumI[i] <- (plotdata$y.L[i-1]*rand_sigma*rand_rho + rand_mu*epsilon*plotdata$y.A[i-1]) 
finalcumI <-sum(plotdata$cumI)

#Cumulative number of Latent quarantined L_q)
  # dL_q <-lambda*beta*c*S*(I+A) - L_q*sigma
lambda  <-params[4]
plotdata$cumL_q<-NA
plotdata$cumL_q[1]<-plotdata$y.L_q[1]
for(i in 2:n)
  plotdata$cumL_q[i] <- (lambda*rand_beta*rand_c*plotdata$y.S[i-1]*(plotdata$y.A[i-1]+plotdata$y.I[i-1]))
finalcumL_q <-sum(plotdata$cumL_q)

#Cumulative number of recovered (R)

#Cumulative number of Hospitalized-home (H-H)

#Cumulative number of dead (D)

# Epidemic duration (Between the firts case (I or A) and the last case lreleased by the H-H compartiment

# Date of the maximum number of cases (I)

#Maximum number of cases (I)


# R(t) or R(0)




######################################################################################################

# validation

#calculation of the number of hopitalised that are dying at each time step and then we compare
#to the final number of dead peopple. The difference should be 0.

n<-nrow(plotdata)

plotdata$test<-NA
for(i in 1:n)
  plotdata$test[i] <- (plotdata$y.H[i]*0.046)

finalstat <-sum(plotdata$test)
plotdata$y.D[365]-finalstat





#finalcumI <-sum(plotdata$cumI)

d<-read.table("WuhanFirstPart.txt",header = T)


plotdata <- data.frame(x=t, y=out)

plotdata <-data.frame(plotdata$y.time,plotdata$y.I,plotdata$y.A)
names(plotdata)[names(plotdata) == "plotdata.y.time"] <- "time"
names(plotdata)[names(plotdata) == "plotdata.y.I"] <- "Inf"
names(plotdata)[names(plotdata) == "plotdata.y.A"] <- "Asym"

d2 <- data.frame(d)
plotdata2 <-merge (plotdata,d2, by='time', all = TRUE)

matplot(x = plotdata2[,c("time")], y = plotdata2[,c("Inf","Asym","casesL")], type = "l",
        xlab = "Time", ylab = "individuals", main = "Model comparison",
        lwd = 1, lty = 1, bty = "l", col = 2:11)

legend(250, 400000, c("Inf sim", "Asym sim","cases obs"), pch = 1, col = 2:11, bty = "n")