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library(bbmle)

library(deSolve)

data1 = c(106, 121, 136, 156, 183, 248, 279, 276, 239, 185, 160, 187, 150, 193, 153, 153, 138, 143, 119)

t1 = c(0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18)

base1 = c(105.1240, 106.3563, 107.5804, 108.7790, 109.9351, 111.0325, 112.0557, 112.9902, 113.8230, 114.5424, 115.1383, 115.6027, 115.9291, 116.1133, 116.1530, 116.0481, 115.8005, 115.4142, 114.8952)

model_SIR = function(t, theta) {

SIR = function(Time, State, Pars) {
with(as.list(c(State, Pars)), {

	DecreaseS = -1 * beta * S * I / N
	DecreaseI = -1 * alpha * I

	dS = DecreaseS
	dI = -1 * DecreaseS + DecreaseI

	return(list(c(dS, dI)))
	})
}	

with(as.list(theta), {
	
state1 = c(S = N - I1, I = I1)	
pars1 = c(beta = beta1, alpha = alpha1, N = N)

state2 = c(S = N - I2, I = I2)	
pars2 = c(beta = beta2, alpha = alpha1, N = N)
	
out1 = ode(y = state1, times = t, func = SIR, parms = pars1, 	method = 'ode45')

out2 = ode(y = state2, times = t, func = SIR, parms = pars2, 	method = 'ode45')

	return(cbind(-diff(out1[,"S"]), -diff(out2[,"S"])))
})

}

loglik_negbin = function(theta, data, mean) {

# for negative bimonial, mean = r p /(1-p)
r = theta[["r"]];

# if r < 0, return a tiny likelihood
if (r < 0)
{
	return(-1e10)
}

sum(dnbinom(x=data, size=r, mu=mean, log=TRUE))

}

loglik_poisson = function(theta, data, mean) {

sum(dpois(x=data, lambda=mean, log=TRUE))

}

SIR_fit_given_logL = function(times, data, base, theta0, model, logL) { # construct a general negative log-likelyhood function

L <- function()
{
	# reconstruct the vector of named pairs of 
	# parameters from the list of arguments
	l=length(theta0)
	theta=c()
	vars=names(theta0)
	
	for (i in 1:l) 
	{
		item=c(x=get(vars[i]))
		names(item) <- vars[i]
		theta <-c(theta, item)
	}
	
	N = theta[["N"]]
      
      if(N < sum(data))
	{
		return(1e10)
	}
	
	for(i in 1:length(theta))
	{
		if(theta[[i]] < 0)
		{
			return(1e10)
		}
	}
	
	l = model(times, theta)
	
	#"base" is the vector of baseline values
	mean = l[,1] + l[,2] + base
	
	# compute the negative log-likelihood
	L = -logL(theta, data, mean)
	# if not a number, return a very small likelihood
	if (is.na(L)) 
	{
		return(1e10)
	}
	
	return(L)
}

# replace the input arguments of L by the list of parameters formals(L)←as.list(theta0) # mle2 # sometimes confint may find a better solution. # In this case we need to refit the model with the better # solution as a starting paoint, because the parameter # names in the returned better fit can be wrong fit = mle2(L, method = “BFGS”, start = as.list(theta0), control = list(maxit = 1e6*length(theta0))) # fit = mle2(L, method = “Nelder-Mead”, start = as.list(theta0), control = list(maxit = 1e6*length(theta0), ndeps = 1e-4, reltol = 1e-10)) # if there is only one parameter to be fitted # the returned confidence interval is a vector # change it to a matrix return(fit) }

SIR_fit = function(times, data, base, theta0, model) {

# we start with negative binomial

if (is.na(theta0['r']))
{
	theta0 = c(theta0, r = 760)
}
	
while (TRUE) 
{
	no_r = is.na(theta0['r']);
	
	if (!no_r)
	{
	 	p = SIR_fit_given_logL(times, data, base, theta0, model, loglik_negbin)
	 
	 }
	 	
	# then it is approximately poisson 
	# in this case we use poisson
	
	r1 = coef(p)["r"]
	
	if (no_r || r1[["r"]] > 10000) {
		# we need to remove r from theta
		if (!no_r) {
			old_theta0 = coef(p)
			theta0 = c()
			for (i in 1:length(old_theta0))
				if (names(old_theta0[i]) != 'r')
					theta0 = c(theta0, old_theta0[i])
		}
		p = SIR_fit_given_logL(times, data, base, theta0, model, loglik_poisson)
		
	}
	
conf = confint(p)

if(is.vector(conf))
{
	conf = matrix(conf, nrow = 1)
}

if(is.matrix(conf))
{
	break
}

theta0 = coef(conf)
names(theta0) = names(coef(p))

}

return(list(fit=p, conf = conf, r=coef(p)["r"]))

}

c = SIR_fit(c(0:19), data1, base1, c(beta1 = 7, alpha1 = 1, N = (sum(data1)*1.166), I1 = 1, beta2 = 1.2, I2 = 1), model_SIR)

print©

aicc = AICc(c"fit", nobs = length(data1))

print(aicc)