SEIRbNosubs.mdl

{UTF-8}
********************************************************
	.seirb-ready
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	|

Indicated Death Rate[States]=
	Simulated Death Rate Data/Population*Normalized population size[States]
	~	Person/Day
	~	Note that the "Data" for deaths is driving the risk perception (because \
		that is what largely influenced public perception of risk)
	|

Simulated Onset Data=
	(1+RANDOM NORMAL(-1, 1 , 0 , 1, NSeed)*Onset Measurement Noise Scale )*onset[s1]
	~	Person/Day
	~		|

Patient Zero Arrival Time=
	20
	~	Day [0,200]
	~	The day on which the first infected person appears in the model.
	|

Death Measurement Noise Scale=
	0.1
	~	dmnl [0,0.3]
	~		|

death rate[States]=
	removing[States]*IFR
	~	Person/Day
	~		|

PWRisk Gamma=
	2
	~	dmnl
	~	"Death risk diminishing impact"
	|

Simulated Death Rate Data=
	(1+RANDOM NORMAL(-1, 1 , 0 , 1, NSeed)*Death Measurement Noise Scale )*death rate[s1\
		]
	~	Person/Day
	~		|

Recovery Measurement Noise Scale=
	0.1
	~	dmnl [0,0.3]
	~		|

recovery rate[States]=
	removing[States]*(1-IFR)
	~	Person/Day
	~		|

IFR=
	0.01
	~	dmnl [0,0.04,0.0005]
	~	The fraction of infections that result in fatality.
	|

Impact of perceived risk on attack rate[States]=
	1/(1+("death rate perceived (lagged death rate)"[States]*Sensitivity to death Alpha)\
		^PWRisk Gamma)
	~	dmnl
	~		|

"Indicated Attack Rate (Transmission intensity)"[States]=
	Transmission intensity Beta*Impact of perceived risk on attack rate[States]
	~	1/Day
	~		|

Time to reduce risk=
	50
	~	Day
	~		|

Time to Perceive Risk[States]=
	(if then else(Indicated Death Rate[States]>"death rate perceived (lagged death rate)"\
		[States],
	Time to perceive Tp,Time to reduce risk))
	~	Day
	~		|

Simulated Recovery Data=
	(1+RANDOM NORMAL(-1, 1 , 0 , 1, NSeed)*Recovery Measurement Noise Scale )*recovery rate\
		[s1]
	~	Person/Day
	~		|

Susceptible Fraction[States]=
	S[States]/(Population-Dead[States])
	~	dmnl
	~	The fraction of the total population that is susceptible to disease - the \
		denominator reflects the complete population less the cumulative deaths.
	|

Transmission intensity Beta=
	0.5
	~	1/Day [0,5,0.05]
	~		|

S[States]= INTEG (
	-exposure[States],
		Population -1)
	~	Person
	~	Population of individuals susceptible to the disease - mutually exclusive \
		of both exposed and infected individuals.
	|

Onset Measurement Noise Scale=
	0.1
	~	dmnl [0,0.3]
	~		|

Sensitivity to death Alpha=
	1
	~	Day/Person [0,2,0.01]
	~	Hazhir estimates Alpha=0.14 for death in million..
	|

Time to perceive Tp=
	30
	~	Day [0,100,5]
	~	7
	|

Parameter Upper Bounds[Params]=
	0.01, 100, 4, 5, 400, 100, 100
	~	
	~		|

AutoCrr Noise 1[States]= INTEG (
	Change in Auto Noise 1[States],
		0)
	~	Dimensionless
	~	Pink Noise is first-order autocorrelated noise.  Pink noise provides a realistic \
		noise input to
		        models in which the next random shock depends in part on the previous \
		shocks.  The user
		        can specify the correlation time.  The mean is 0 and the standard deviation \
		is specified
		         by the user.
	|

Change in Auto Noise 1[States]=
	(White Noise 1[States] - AutoCrr Noise 1[States])/Noise Correlation Time 1
	~	1/Day
	~	Change in the pink noise value; Pink noise is a first order exponential smoothing \
		delay of the white
		         noise input.
	|

Noise Correlation Time 1=
	10
	~	Day [1,20]
	~	The correlation time constant for Pink Noise.
	|

ProcessNoiseExposure[States]=
	Max(0,Min(2,1+Switch for process noise*AutoCrr Noise 1[States]))
	~	dmnl
	~		|

NSeed=
	1
	~	dmnl
	~		|

White Noise 1[States]=
	Noise Standard Deviation 1*((2-TIME STEP/Noise Correlation Time 1)/(TIME STEP/Noise Correlation Time 1\
		))^0.5*RANDOM NORMAL(-10, 10 , 0 , 1 , NSeed )
	~	Dimensionless
	~	White noise input to the pink noise process.
	|

Noise Standard Deviation 1=
	0.05
	~	Dimensionless [0,1]
	~	The standard deviation of the pink noise process.
	|

Dead[States]= INTEG (
	death rate[States],
		0)
	~	Person
	~		|

"death rate perceived (lagged death rate)"[States]= INTEG (
	(Indicated Death Rate[States]-"death rate perceived (lagged death rate)"[States])/Time to Perceive Risk\
		[States],
		Indicated Death Rate[States])
	~	Person/Day
	~		|

E[States]= INTEG (
	exposure[States]-onset[States]+Patient Zero Arrival[States],
		0)
	~	Person
	~		|

exposure[States]=
	I[States]*"Indicated Attack Rate (Transmission intensity)"[States]*Susceptible Fraction\
		[States]*ProcessNoiseExposure[States]
	~	Person/Day
	~		|

I[States]= INTEG (
	-death rate[States]+onset[States]-recovery rate[States],
		0)
	~	Person
	~	The population currently infected with the disease.
	|

Normalized Estimated Parameters[Params]=
	1,0.002,0.23,0.4,0.23,0.14,0.33
	~	
	~		|

Normalized population size[States]=
	1e+06
	~	Person
	~	The
	|

onset[States]=
	E[States]/"Time to onset (Te)"[States]*Onset DATA WRONG HELP[States]
	~	Person/Day
	~		|

Onset DATA WRONG HELP[States]=
	1
	~	dmnl
	~	CURRENTLY DIMENSIONLESS AND WRONG
	|

Parameter Lower Bounds[Params]=
	0.003,0.01,0.1,0,10, 1, 0
	~	
	~		|

Params:
	IFRt, SnsTDth, TrnInts, PWRskMlt, TmRdRsk, TmPrc, Ptn0Arr
	~	
	~		|

Patient zero[States]=
	1
	~	Person
	~	The first person who is infected (can be increased such that more than one \
		person at a time arrive).
	|

Patient Zero Arrival[States]=
	if then else ( Time 
	                  < Patient Zero Arrival Time 
	                  :AND: Time 
	                       + TIME STEP 
	                       >= Patient Zero Arrival Time, 
	             Patient zero[States] 
	                  / TIME STEP , 
	             0)
	~	Person/Day
	~	Rate of increase in exposed individuals due to infected individuals \
		entering the system.
	|

Population=
	1e+06
	~	Person
	~	99,1;99,1; Total population - set equal to an initial constant. This is \
		not endogenously growing or declining.
	|

Recovered[States]= INTEG (
	recovery rate[States],
		0)
	~	Person
	~	Population that has had and then subsequently recovered from infection.
	|

removing[States]=
	I[States]/"Time to removal (Tr)"[States]
	~	Person/Day
	~		|

States:
	s1
	~	
	~	Subscript representing the 50 US States. DC excluded
	|

Switch for process noise=
	1
	~	dmnl [0,1,1]
	~		|

"Time to onset (Te)"[States]=
	4
	~	Day [0,10,1]
	~	The number of days after exposure at which infection begins
	|

"Time to removal (Tr)"[States]=
	10
	~	Day
	~		|

********************************************************
	.Control
********************************************************~
		Simulation Control Parameters
	|

FINAL TIME  = 600
	~	Day
	~	The final time for the simulation.
	|

INITIAL TIME  = 0
	~	Day
	~	The initial time for the simulation.
	|

SAVEPER  = 1
	~	Day [0,?]
	~	The frequency with which output is stored.
	|

TIME STEP  = 0.25
	~	Day [0,?]
	~	The time step for the simulation.
	|

\\\---/// Sketch information - do not modify anything except names
V300  Do not put anything below this section - it will be ignored
*View 1
$192-192-192,0,Arial|11||0-0-0|0-0-0|0-0-255|255-255-255|255-255-255|96,96,74,0
10,1,S,577,461,40,20,3,3,0,0,0,0,0,0,0,0,0,0,0,0
10,2,E,901,463,40,20,3,3,0,0,0,0,0,0,0,0,0,0,0,0
10,3,I,1170,461,40,16,3,3,0,0,0,0,0,0,0,0,0,0,0,0
10,4,Recovered,1479,367,40,20,3,3,0,0,0,0,0,0,0,0,0,0,0,0
1,5,7,2,4,0,0,22,0,0,0,-1--1--1,,1|(801,462)|
1,6,7,1,100,0,0,22,0,0,0,-1--1--1,,1|(673,462)|
11,7,0,736,462,6,8,34,3,0,0,1,0,0,0,0,0,0,0,0,0
10,8,exposure,736,479,31,9,40,3,0,0,-1,0,0,0,0,0,0,0,0,0
1,9,11,3,4,0,0,22,0,0,0,-1--1--1,,1|(1088,462)|
1,10,11,2,100,0,0,22,0,0,0,-1--1--1,,1|(987,462)|
11,11,0,1040,462,6,8,34,3,0,0,1,0,0,0,0,0,0,0,0,0
10,12,onset,1040,479,20,9,40,3,0,0,-1,0,0,0,0,0,0,0,0,0
1,13,1,45,1,0,43,0,0,128,0,-1--1--1,,1|(573,511)|
10,14,Transmission intensity Beta,681,839,62,30,8,131,0,2,0,0,0,0,0-0-0,0-0-0,|||255-0-0,0,0,0,0,0,0
1,15,2,11,1,0,43,0,0,128,0,-1--1--1,,1|(1027,430)|
10,16,"Time to onset (Te)",1016,343,46,16,8,3,0,2,0,0,0,0,0-0-0,0-0-0,|||0-128-0,0,0,0,0,0,0
10,17,"Time to removal (Tr)",1592,454,42,16,8,3,0,2,0,0,0,0,0-0-0,0-0-0,|||0-128-0,0,0,0,0,0,0
1,18,16,11,1,0,45,0,0,128,0,-1--1--1,,1|(1047,416)|
10,19,IFR,1206,561,13,9,8,3,0,2,0,0,0,0,0-0-0,0-0-0,|||255-0-0,0,0,0,0,0,0
1,20,19,36,0,0,0,0,0,128,0,-1--1--1,,1|(0,0)|
10,21,"death rate perceived (lagged death rate)",1109,718,53,30,3,3,0,0,0,0,0,0,0,0,0,0,0,0
10,22,Impact of perceived risk on attack rate,934,665,61,31,8,131,0,0,0,0,0,0,0,0,0,0,0,0
1,23,21,22,1,0,0,0,0,128,0,-1--1--1,,1|(1048,708)|
10,24,Time to perceive Tp,1158,854,75,23,8,131,0,2,0,0,0,0,0-0-0,0-0-0,|||255-0-0,0,0,0,0,0,0
10,25,Sensitivity to death Alpha,820,829,49,23,8,131,0,2,-1,0,0,0,0-0-0,0-0-0,|||255-0-0,0,0,0,0,0,0
1,26,25,22,0,0,0,0,0,64,0,-1--1--1,,1|(0,0)|
1,27,3,8,1,0,43,0,0,64,0,-1--1--1,,1|(997,524)|
10,28,Dead,1483,530,40,16,3,3,0,0,0,0,0,0,0,0,0,0,0,0
1,29,31,4,4,0,0,22,0,0,0,-1--1--1,,1|(1400,366)|
1,30,31,3,100,0,0,22,0,0,0,-1--1--1,,1|(1170,366)|
11,31,0,1355,366,6,8,34,3,0,0,1,0,0,0,0,0,0,0,0,0
10,32,recovery rate,1355,383,44,9,40,131,0,0,-1,0,0,0,0,0,0,0,0,0
1,33,35,28,4,0,0,22,0,0,0,-1--1--1,,1|(1393,535)|
1,34,35,3,100,0,0,22,0,0,0,-1--1--1,,1|(1170,535)|
11,35,0,1338,535,6,30,34,3,0,0,1,0,0,0,0,0,0,0,0,0
10,36,death rate,1338,552,35,9,40,131,0,0,-1,0,0,0,0,0,0,0,0,0
10,37,removing,1376,455,31,9,8,3,0,0,0,0,0,0,0,0,0,0,0,0
1,38,3,37,0,0,43,0,0,64,0,-1--1--1,,1|(0,0)|
1,39,17,37,0,0,45,0,0,64,0,-1--1--1,,1|(0,0)|
1,40,37,32,1,0,43,0,0,128,0,-1--1--1,,1|(1395,420)|
1,41,37,35,1,0,43,0,0,128,0,-1--1--1,,1|(1384,487)|
10,42,IFR,1304,306,21,9,8,2,0,3,-1,0,0,0,128-128-128,0-0-0,|||128-128-128,0,0,0,0,0,0
1,43,42,31,0,0,45,0,0,128,0,-1--1--1,,1|(0,0)|
10,44,"Indicated Attack Rate (Transmission intensity)",796,582,62,30,8,3,0,0,0,0,0,0,0,0,0,0,0,0
10,45,Susceptible Fraction,599,547,39,16,8,3,0,0,0,0,0,0,0,0,0,0,0,0
1,46,22,44,1,0,43,0,0,128,0,-1--1--1,,1|(868,640)|
1,47,14,44,1,0,43,0,0,128,0,-1--1--1,,1|(682,710)|
1,48,45,8,1,0,43,0,0,128,0,-1--1--1,,1|(675,547)|
10,49,Population,414,480,36,9,8,3,0,2,-1,0,0,0,0-0-0,0-0-0,|||128-0-128,0,0,0,0,0,0
1,50,49,1,0,0,0,0,0,128,1,-1--1--1,,1|(0,0)|
1,51,49,45,0,0,45,0,0,128,0,-1--1--1,,1|(0,0)|
10,52,Population,1421,693,44,9,8,2,0,3,-1,0,0,0,128-128-128,0-0-0,|||128-128-128,0,0,0,0,0,0
10,53,Indicated Death Rate,1313,648,39,16,8,3,0,0,-1,0,0,0,0,0,0,0,0,0
1,54,53,21,0,0,0,0,0,64,0,-1--1--1,,1|(0,0)|
1,55,52,53,0,0,0,0,0,128,0,-1--1--1,,1|(0,0)|
10,56,Time to reduce risk,1331,898,37,16,8,3,0,2,-1,0,0,0,0-0-0,0-0-0,|||255-0-0,0,0,0,0,0,0
10,57,Patient Zero Arrival Time,782,250,41,16,8,131,0,2,-1,0,0,0,0-0-0,0-0-0,|||255-0-0,0,0,0,0,0,0
11,58,0,879,375,8,7,33,3,0,0,2,0,0,0,0,0,0,0,0,0
10,59,Patient Zero Arrival,830,375,41,16,40,3,0,0,-1,0,0,0,0,0,0,0,0,0
1,60,57,59,0,0,0,0,0,64,0,-1--1--1,,1|(0,0)|
12,61,48,879,311,25,15,0,3,0,0,-1,0,0,0,0,0,0,0,0,0
1,62,58,61,100,0,0,22,0,0,0,-1--1--1,,1|(879,347)|
1,63,58,2,4,0,0,22,0,0,0,-1--1--1,,1|(879,412)|
10,64,Time,731,347,26,9,8,2,0,3,-1,0,0,0,128-128-128,0-0-0,|||128-128-128,0,0,0,0,0,0
1,65,64,59,0,0,0,0,0,64,0,-1--1--1,,1|(0,0)|
10,66,TIME STEP,726,306,46,9,8,2,0,3,-1,0,0,0,128-128-128,0-0-0,|||128-128-128,0,0,0,0,0,0
1,67,66,59,0,0,0,0,0,64,0,-1--1--1,,1|(0,0)|
10,68,PWRisk Gamma,939,847,64,23,8,3,0,2,-1,0,0,0,0-0-0,0-0-0,|||255-0-0,0,0,0,0,0,0
1,69,68,22,0,0,0,0,0,64,0,-1--1--1,,1|(0,0)|
1,70,44,8,0,0,43,0,0,128,0,-1--1--1,,1|(0,0)|
10,71,Normalized population size,1178,609,50,16,8,3,0,2,-1,0,0,0,0-0-0,0-0-0,|||0-128-0,0,0,0,0,0,0
1,72,71,53,0,0,0,0,0,64,0,-1--1--1,,1|(0,0)|
10,73,Patient zero,868,262,40,9,8,3,0,0,-1,0,0,0,0,0,0,0,0,0
1,74,73,59,0,0,0,0,0,64,0,-1--1--1,,1|(0,0)|
10,75,Time to Perceive Risk,1294,756,59,20,8,3,0,0,-1,0,0,0,0,0,0,0,0,0
1,76,75,21,0,0,0,0,0,64,0,-1--1--1,,1|(0,0)|
1,77,21,75,1,0,0,0,0,64,0,-1--1--1,,1|(1197,732)|
1,78,53,75,0,0,0,0,0,64,0,-1--1--1,,1|(0,0)|
1,79,24,75,0,0,0,0,0,64,0,-1--1--1,,1|(0,0)|
1,80,56,75,0,0,0,0,0,64,0,-1--1--1,,1|(0,0)|
10,81,Dead,571,613,27,9,8,2,0,2,-1,0,0,0,-1--1--1,-1--1--1,|||128-128-128,0,0,0,0,0,0
1,82,81,45,0,0,45,0,0,128,0,-1--1--1,,1|(0,0)|
10,83,Onset DATA WRONG HELP,1113,338,49,23,8,3,0,0,-1,0,0,0,0,0,0,0,0,0
1,84,83,11,1,0,0,0,0,192,0,-1--1--1,,1|(1110,399)|
10,85,Switch for process noise,447,345,55,23,8,3,1,2,-1,0,0,0,0-0-0,0-0-0,|||128-128-0,0,0,0,0,0,0
10,86,ProcessNoiseExposure,636,371,88,23,8,3,1,0,-1,0,0,0,0,0,0,0,0,0
1,87,86,8,0,1,0,0,0,64,0,-1--1--1,,1|(0,0)|
10,88,Simulated Recovery Data,1429,280,63,23,8,3,1,2,-1,0,0,0,0-0-0,0-0-0,|||255-128-0,0,0,0,0,0,0
12,89,0,2127,382,389,231,8,79,0,0,1,0,0,0,0,0,0,0,0,0
SEIR
12,90,0,2126,1000,445,309,8,79,0,0,2,0,0,0,0,0,0,0,0,0
exposure,Graph
10,91,Normalized Estimated Parameters,750,1072,46,23,8,3,0,0,-1,0,0,0,0,0,0,0,0,0
10,92,Parameter Upper Bounds,1066,1120,56,23,8,3,0,0,-1,0,0,0,0,0,0,0,0,0
10,93,Parameter Lower Bounds,1302,1026,56,23,8,3,0,0,-1,0,0,0,0,0,0,0,0,0
12,94,0,2971,265,341,230,8,79,0,0,2,0,0,0,0,0,0,0,0,0
Dead[States],Graph
10,95,Simulated Onset Data,1038,224,63,23,8,3,0,2,-1,0,0,0,0-0-0,0-0-0,|||255-128-0,0,0,0,0,0,0
1,96,11,95,1,0,0,0,0,192,0,-1--1--1,,1|(1060,289)|
10,97,Simulated Death Rate Data,1446,639,63,23,8,3,0,2,-1,0,0,0,0-0-0,0-0-0,|||255-128-0,0,0,0,0,0,0
1,98,36,97,0,0,0,0,0,192,0,-1--1--1,,1|(0,0)|
10,99,Recovery Measurement Noise Scale,1612,339,66,24,8,3,0,2,-1,0,0,0,0-0-0,0-0-0,|||255-0-0,0,0,0,0,0,0
1,100,99,88,0,0,0,0,0,64,0,-1--1--1,,1|(0,0)|
10,101,NSeed,1339,213,36,9,8,3,0,0,-1,0,0,0,0,0,0,0,0,0
1,102,101,88,0,0,0,0,0,64,0,-1--1--1,,1|(0,0)|
1,103,32,88,0,0,0,0,0,64,0,-1--1--1,,1|(0,0)|
10,104,Death Measurement Noise Scale,1616,651,46,24,8,3,0,2,-1,0,0,0,0-0-0,0-0-0,|||255-0-0,0,0,0,0,0,0
1,105,104,97,0,0,0,0,0,64,0,-1--1--1,,1|(0,0)|
1,106,101,97,1,0,0,0,0,64,0,-1--1--1,,1|(1690,344)|
1,107,101,95,0,0,0,0,0,64,0,-1--1--1,,1|(0,0)|
10,108,Onset Measurement Noise Scale,903,154,46,24,8,3,0,2,-1,0,0,0,0-0-0,0-0-0,|||255-0-0,0,0,0,0,0,0
1,109,108,95,0,0,0,0,0,64,0,-1--1--1,,1|(0,0)|
10,110,AutoCrr Noise 1,639,58,34,23,3,3,0,0,0,0,0,0,0,0,0,0,0,0
12,111,48,434,64,25,15,0,3,0,0,-1,0,0,0,0,0,0,0,0,0
10,112,White Noise 1,361,180,53,19,8,3,0,0,0,0,0,0,0,0,0,0,0,0
10,113,Noise Standard Deviation 1,300,285,52,16,8,3,0,2,0,0,0,0,0-0-0,0-0-0,|||251-2-7,0,0,0,0,0,0
11,114,0,533,64,6,8,34,3,0,0,1,0,0,0,0,0,0,0,0,0
10,115,Change in Auto Noise 1,533,88,52,16,40,3,0,0,0,0,0,0,0,0,0,0,0,0
10,116,Noise Correlation Time 1,313,53,58,16,8,3,0,2,0,0,0,0,0-0-0,0-0-0,|||251-2-7,0,0,0,0,0,0
1,117,114,110,4,0,0,22,0,0,0,-1--1--1,,1|(572,64)|
1,118,114,111,100,0,0,22,0,0,0,-1--1--1,,1|(493,64)|
1,119,110,114,2,0,0,0,0,0,0,-1--1--1,,1|(597,13)|
1,120,112,115,2,0,0,0,0,0,0,-1--1--1,,1|(438,143)|
1,121,116,115,2,0,0,0,0,0,0,-1--1--1,,1|(428,99)|
1,122,116,112,1,0,0,0,0,0,0,-1--1--1,,1|(303,139)|
1,123,113,112,1,0,0,0,0,0,0,-1--1--1,,1|(342,223)|
1,124,101,112,1,0,0,0,0,64,0,-1--1--1,,1|(886,107)|
10,125,TIME STEP,166,180,46,9,8,2,0,3,-1,0,0,0,128-128-128,0-0-0,|||128-128-128,0,0,0,0,0,0
1,126,125,112,0,0,0,0,0,64,0,-1--1--1,,1|(0,0)|
1,127,110,86,0,0,0,0,0,192,0,-1--1--1,,1|(0,0)|
1,128,85,86,0,0,0,0,0,64,0,-1--1--1,,1|(0,0)|
1,129,97,53,0,0,0,0,0,192,0,-1--1--1,,1|(0,0)|
12,130,0,3001,891,401,396,8,15,0,0,1,0,0,0,0,0,0,0,0,0
GRAPH
///---\\\
:GRAPH SEIR
:TITLE SEIR
:X-AXIS Time
:SCALE
:VAR E
:DATASET 
:SCALE
:VAR I
:DATASET 
:SCALE
:VAR S
:DATASET 
:SCALE
:VAR Recovered
:DATASET 
:SCALE
:VAR Dead
:DATASET 

:GRAPH GRAPH
:TITLE Data Outputs 
:SCALE
:VAR Simulated Death Rate Data
:DATASET 
:SCALE
:VAR Simulated Onset Data
:DATASET 
:VAR Simulated Recovery Data
:DATASET 
:L<%^E!@
1:Test3.vdfx
4:Time
5:exposure[States]
6:IFRt
6:s1
9:Test3
19:74,0
24:0
25:600
26:600
23:0
15:0,0,0,0,0,0
27:0,
34:0,
42:1
72:0
73:0
35:Date
36:YYYY-MM-DD
37:2000
38:1
39:1
40:2
41:0
95:0
96:0
97:0
77:0
78:0
102:0
93:0
94:0
92:0
91:0
90:0
87:0
75:
43:
103:8,8,8,3,8
105:0,0,0,0,0,0,0,0,0,0
104:Arial|12||0-0-0|0-0-0|-1--1--1|0-0-255|192-192-192|-1--1--1