# basicplus.model
# Facilitated Systems
# http://facilitatedsystems.com/
# 2007-03-27

States = {
  NotYet,  # Groups who have not yet become concert-goers
  Now,     # Current concert-goers
  NoMore   # Past concert-goers
};

Outputs = {
  NewConcertGoers_PA,
  DepartingConcertGoers_PA,
  ReproductionRate,
  Population,
  NotYetBirths_PA,
  NowBirths_PA,
  NoMoreBirths_PA,
  NotYetDeaths_PA,
  NowDeaths_PA,
  NoMoreDeaths_PA,
  NotYetImmigration_PA,
  NowImmigration_PA,
  NoMoreImmigration_PA
};

InitialNotYet =     90.0e6;
InitialNow =        10.0e6;
InitialNoMore =        0.0;

Immigration_PA         = 2.0e6;
FractNotYetImmigration = 0.90;
FractNowImmigration    = 0.10;
FractNoMoreImmigration = 0.00;

Fecundity = 2.1;   # births per female 

Lifespan = 75.0;   # years

Contacts_PA =      40.0;
Infectiousness =   1.0 / 900.0;
FractionDeparting_PA = 0.04;
AdvertisingIntensity = 1.0;   # Relative intensity of advertising effort DMNL
AdvertisingEffectiveness = 0.0005;   # 1 / YEAR

Initialize{
  NotYet = InitialNotYet;
  Now = InitialNow;
  NoMore = InitialNoMore;
}

Dynamics{
  Population = NotYet + Now + NoMore;
  WOM_PA =
    Contacts_PA * (Now / Population)
    * Infectiousness * NotYet;
  Advertising_PA = NotYet * AdvertisingIntensity * AdvertisingEffectiveness;
  NewConcertGoers_PA = WOM_PA + Advertising_PA;
  DepartingConcertGoers_PA = 
    Now * FractionDeparting_PA;

  # Births #############################################################

  # Births out of one group don't have to go back to that group.

  NotYetBirths_PA = Fecundity * NotYet / (Lifespan - 40);
  NowBirths_PA = Fecundity * Now / (Lifespan - 40);
  NoMoreBirths_PA = Fecundity * NoMore / (Lifespan - 40);

  # Immigration ########################################################

  NotYetImmigration_PA = FractNotYetImmigration * Immigration_PA;
  NowImmigration_PA    = FractNowImmigration * Immigration_PA;
  NoMoreImmigration_PA = FractNoMoreImmigration * Immigration_PA;

  # Deaths #############################################################

  NotYetDeaths_PA = NotYet / Lifespan;
  NowDeaths_PA    = Now    / Lifespan;
  NoMoreDeaths_PA = NoMore / Lifespan;

  ######################################################################
  dt(NotYet) = (NotYetImmigration_PA + NotYetBirths_PA)
	- (NewConcertGoers_PA + NotYetDeaths_PA);
  dt(Now) = (NowImmigration_PA + NowBirths_PA +NewConcertGoers_PA) 
    - (DepartingConcertGoers_PA + NowDeaths_PA);	
  dt(NoMore) = (NoMoreImmigration_PA + NoMoreBirths_PA + 
	DepartingConcertGoers_PA)
	- (NoMoreDeaths_PA);
}

CalcOutputs{
  ReproductionRate = 
    Contacts_PA * Infectiousness
    * (1.0 / FractionDeparting_PA) * (NotYet/Population);
}