SEIR-Model-Periodic-Transmission

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globals 
[ 
  maximum-infectious           ;; The maximum number of infectious individuals at one simulation tick.  
  tick-at-maximum-infectious   ;; The first tick when the maximum number of infectious individuals is realized.  
  number-infectious-vector     ;; Vector of the number of infectious individuals for each simulation tick.  
  
  incubation-alpha             ;; Alpha parameter for the gamma distribution used in calculating incubation-time.
  incubation-lambda            ;; Lambda parameter for the gamma distribution used in calculating incubation-time.
  infectious-alpha             ;; Alpha parameter for the gamma distribution used in calculating infectious-time.
  infectious-lambda            ;; Lambda parameter for the gamma distribution used in calculating infectious-time. 
  
  periodic-transmission-chance
]

turtles-own
[ 
  susceptible?                 ;; If true, the individual is a member of the susceptible class.  
  exposed?                     ;; If true, the individual is a member of the exposed (incubation) class.
  infectious?                  ;; If true, the individual is a member of the infectious class.
  recovered?                   ;; If true, the individual is a member of the recovered class.
  
  incubation-length            ;; How long the individual has been in the exposed class, increasing by 1 each tick. This is compared against the incubation-time, selected from a gamma-distribution.
  incubation-time              ;; The randomly chosen gamma-distribution value for how long the individual will be in the exposed class.
  infectious-length            ;; How long the individual has been in the infectious class, increasing by 1 each tick. This is compared against the infectious-time, selected from a gamma-distribution.
  infectious-time              ;; The randomly chosen gamma-distribution value for how long the individual will be in the infectious class.
  
  total-contacts               ;; A count of all contacts of the individual.
]

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;;;; Setup Procedures ;;;;

to setup
  clear-all
  setup-gamma-distributions
  setup-population
  reset-ticks 
end 

to setup-gamma-distributions            ;; The calculation from mean and standard deviation (in days) to the alpha and lambda parameters required for the gamma-distributions (in ticks).  
  set incubation-alpha (average-incubation-period * ticks-per-day)^ 2 / (incubation-standard-deviation * ticks-per-day)^ 2    
  set incubation-lambda (average-incubation-period * ticks-per-day) / (incubation-standard-deviation * ticks-per-day)^ 2      
  set infectious-alpha (average-infectious-period * ticks-per-day)^ 2 / (infectious-standard-deviation * ticks-per-day)^ 2    
  set infectious-lambda (average-infectious-period * ticks-per-day) / (infectious-standard-deviation * ticks-per-day)^ 2   
end 

to setup-population
  create-turtles initial-population   
  [
    setxy random-xcor random-ycor       ;; All individuals are placed on random patches in the world.
    
    set susceptible? true               ;; All individuals are set as susceptible.
    set exposed? false      
    set infectious? false       
    set recovered? false   
   
    set shape "person"
    
    set total-contacts 0
    
    ask turtle 0                        ;; Individual 0 begins as infectious.  Its infectious-time is selected from the gamma distribution and infectious-length set to 0.  
    [
      set susceptible? false
      set infectious? true
      set infectious-time random-gamma infectious-alpha infectious-lambda
      set infectious-length 0
    ]
    
   set number-infectious-vector [ 1 ]   ;; The number-infectious-vector vector is initiallized.  
   assign-color
   set periodic-transmission-chance ( average-transmission-chance - minimum-transmission-chance ) * sin((360 / (365 * ticks-per-day)) * (0 - ( month-of-maximum-trans-chance + 8 ) * 30 * ticks-per-day)) + ( average-transmission-chance )
  ]
end 

to assign-color
  if susceptible?
    [ set color white ]
  if exposed?
    [ set color yellow ]
  if infectious?           
    [ set color red ]      
  if recovered?            
    [ set color lime ]
end 

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;;;; Go Procedure ;;;;

to go
  if all? turtles [ susceptible? or recovered? ]          ;; The simulation ends when no individuals are infected (exposed or infectious).  
    [ stop ]                                                                                 
  
  ask turtles                                                                        
    [ move ]
    
  ask turtles with [ infectious? ]                        ;; Infectious individuals might expose susceptible neighbors.  If infectious individuals have been infectious for infectious-time ticks, they will recover. 
    [ expose-neighbors 
      chance-of-recovery ]                              
  
  ask turtles with [ exposed? ]                           ;; If exposed individuals have been in the exposed class for incubation-time ticks, they will become infectious.
    [ chance-of-becoming-infectious ]  
     
  ask turtles 
    [ assign-color 
      count-contacts ]

  compute-maximum-infectious  
  
  tick
  
  calculate-periodic-transmission-chance
end 

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;;;; Nested Functions ;;;;

to move                                                                            ;; Individuals turn a random angle between -40 and 40 degrees then step forward 1 unit.  
  right (random 80) - 40
  forward 1
  if not can-move? 1 [ right 180 ]                                                 ;; If an individual is at the world's boundary, it turns around.
end 

to count-contacts                                                                  ;; Contacts are defined as other individuals within a 1 unit radius.  
  set total-contacts total-contacts + count other turtles in-radius 1
end 

to expose-neighbors
  ask other turtles in-radius 1 with [ susceptible? ]                              ;; Susceptible individuals who come into contact with an infectious individual will become infected with probability transmission-chance.
    [ 
      if random-float 100 < periodic-transmission-chance                                            
        [ 
          set susceptible? false  
          set exposed? true                                                                   
          set incubation-time random-gamma incubation-alpha incubation-lambda      ;; A newly exposed individual selects an incubation-time from the gamma-distribution and its incubation-lenth is set to 0.          
          set incubation-length 0                                                          
        ]             
    ]                                                              
end       

to chance-of-becoming-infectious                                                   ;; When an infected individual has been in the exposed class longer than its incubation-time, it will become infectious.  
  set incubation-length incubation-length + 1
  if incubation-length > incubation-time                                     
  [                                                                          
    set exposed? false
    set infectious? true                                                      
    set infectious-time random-gamma infectious-alpha infectious-lambda            ;; A newly infectious individual selects an infectious-time from the gamma-distribution and its infection-length is set to 0.
    set infectious-length 0                                                 
  ]
end 

to chance-of-recovery                                                              ;; When an infectious individual has been in the infectious class longer than its infection-time, it will recover.
  set infectious-length infectious-length + 1
  if infectious-length > infectious-time                                     
  [                                                                          
    set infectious? false
    set recovered? true
  ]
end 

to calculate-periodic-transmission-chance                                          ;; The periodic transmission probability is A sin ( B (t - C) ) + D, for t in ticks.
  set periodic-transmission-chance ( average-transmission-chance - minimum-transmission-chance ) * sin((360 / (365 * ticks-per-day)) * (ticks - ( month-of-maximum-trans-chance + 8 ) * 30 * ticks-per-day)) + (average-transmission-chance )
end 

to compute-maximum-infectious                                                      ;; A vector of the number of infectious individuals at each tick is stored.  The maximum and time of the maximum are computed.  
  set number-infectious-vector lput count turtles with [infectious?] number-infectious-vector
  set maximum-infectious max number-infectious-vector
  set tick-at-maximum-infectious position maximum-infectious number-infectious-vector   
end 

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