globals [ population mortality income mortality-income-coefficient ; coefficient of income-mortality relation threshold ; below this level of income can start the plague probability-start-plague ; probability that a family can start the plague ; when income is beloe threshold level radius-plague ; radius of the plague ] turtles-own [n ; people in each family infect ; boolean ] to setup-turtles set-default-shape turtles "house" create-turtles 5 set threshold 0.0001 set probability-start-plague 0.0005 set radius-plague 2 set mortality-income-coefficient 630 ask turtles [ setxy random-pxcor random-pycor set n 2 set color green set infect false ] end ; check many global variables: population, income mortality to check-globals ask turtles [ if n <= 0 [ die ] if show-label = true [ set label n ] ] set population sum [n] of turtles ifelse population > 0 [ set income 1 / population ; perfect division of income among population set mortality 1 - mortality-income-coefficient * income ; MORTALITY RATE FUNCTION ; mortality is a negative function of income ; and positive function of the coefficient ] [ set income 0 ; just in case the whole population in dead set mortality 0 ; ] end ; for each family start a plague when income is under the threshold level, with a given ; probability ; for each infected family, infect other families with given probability and in a given radius to check-plague ask turtles [ if income < threshold ; threshold level of deprivation [ if infect = false [ if random-float 1 < probability-start-plague [ set infect true set color red ] ] ] if infect = true [ if random-float 1 < probability-of-contagion [ ask turtles in-radius radius-plague [ set infect true set color red ] ] ] ] end ; how many people die in each family to check-death ask turtles [ ifelse infect = false ; natural death [ if random-float 1 < mortality ; to avoid homogeneous population [ set n ceiling ( n - n * mortality ) if show-label = true [ set label n ] ] ] [ set n n - 4 ; effect of the plague ] ] end to check-birth ask turtles [ if infect = false ; otherwise, the family cannot have new members [ set n n + fertility ] if show-label = true [ set label n ] ] end ; a family can split and "hatch" a new one to check-families ask turtles [ if n > 10 [ set n n - 2 hatch 1 [ set n 2 lt random 360 fd random ( 10 - density ) set color green set infect false ] ] if show-label = true [ set label n ] ] end to do-plots set-current-plot "Population" set-current-plot-pen "population" plot population end to setup clear-all setup-turtles end to go check-globals check-plague check-death check-globals check-birth check-families do-plots tick end @#$#@#$#@ GRAPHICS-WINDOW 279 10 796 470 19 16 13.0 1 10 1 1 1 0 0 0 1 -19 19 -16 16 1 1 1 ticks CC-WINDOW 5 487 805 582 Command Center 0 BUTTON 4 10 67 43 setup setup NIL 1 T OBSERVER NIL NIL NIL NIL BUTTON 74 10 137 43 go go T 1 T OBSERVER NIL NIL NIL NIL SLIDER 3 95 175 128 fertility fertility 1 10 5 1 1 NIL HORIZONTAL MONITOR 3 318 65 363 mortality Mortality 5 1 11 MONITOR 74 318 180 363 Income Income 5 1 11 PLOT 3 167 203 317 Population NIL NIL 0.0 10.0 0.0 10.0 true false PENS "default" 1.0 0 -16777216 true "Population" 1.0 0 -13345367 true SLIDER 3 129 175 162 density density 0 10 2 1 1 NIL HORIZONTAL SWITCH 3 440 117 473 show-label show-label 1 1 -1000 SLIDER 3 374 185 407 probability-of-contagion probability-of-contagion 0 1 0.4 0.1 1 NIL HORIZONTAL @#$#@#$#@ WHAT IS IT? ----------- This project simulates demopraphic crisis in a closed economy with no growth, in line with the classic, Malthusian, theory. Our purpose is to emulate simple population trends in a pre-industrial society. Agents in this model are families: their goal is to maximize family income, in order to do so they bear children, according to their fertility. Total income is fixed (and normalized to 1) and every person earn a fraction of it equal to 1/population. When income is below a threshold every family run the risk of starting a terrible plague. Every infect family can infect closer families. HOW TO USE IT ------------- Click the setup button to set up the families. Click the go button to start the simulation. With the slider FERTILITY you can choose how may children each family can bear at the beginning of every period. The slider DENSITY controls the "urban" density, while PROBABILITY OF CONTAGION control how much the plague in dangerous. Turning on SHOW-LABEL you can see how many people live in every family. HOW IT WORKS ------------ During every period in each infect family (red) 4 people die, and every person in the economy can die under a probability equal to MORTALITY. Mortality is inversely proportional to income. When in a family live more than ten people, two of them start a new one. THINGS TO TRY ------------- Setting the slide PROBABILITY OF CONTAGION to zero is a nice experiment. Do the population rises forever? Manipulating the sliders you can see under which conditions the population is doomed to extinction. EXTENDING THE MODEL ------------------- The biggest limit of this model is that agents don't learn anything from the plague (how to protect themselves and their family from a new one). 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