SEIR-Model-Vaccination-Seasonal

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4 collaborators

Default-person Anna Mummert (Author)
Roger Estep (Team member)
Robert Hughes (Team member)
Jessica Shiltz (Team member)

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disease control 

Tagged by Anna Mummert about 1 year ago

gamma distribution 

Tagged by Anna Mummert about 1 year ago

infectious disease model 

Tagged by Anna Mummert about 1 year ago

seasonal vaccination* 

Tagged by Anna Mummert about 1 year ago

seir modelg 

Tagged by Anna Mummert about 1 year ago

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Case Study "Modeling Seasonal Influenza"

This model is part of a suite of infectious disease models, including SEIR-Model-Base-Seasonal, SEIR-Model-Vaccination-Seasonal, SEIR-Model-Antivirals, SEIR-Model-Isolation, and SEIR-Model-Periodic-Transmission. These five models are part of the case study "Modeling Seasonal Influenza", 2016, by Marcia Harrison-Pitaniello, Jessica Shiltz, Rober Hughes, Roger Estep, and Anna Mummert published by the National Center for Case Study Teaching in Science (http://sciencecases.lib.buffalo.edu/cs/).

Posted about 1 year ago

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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 at 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.
  seroconversion-alpha         ;; Alpha parameter for the gamma distribution used in calculating seroconversion-time.
  seroconversion-lambda        ;; Lambda parameter for the gamma distribution used in calculating seroconversion-time.  
  
  number-vaccinated
  
  infection-possible
]

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.
  vaccination?                 ;; If true, the individual has received the vaccine.  
  seroconverted?               ;; If true, the individual has received the vaccine and has seroconverted.  
  
  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.
  seroconversion-length        ;; How long since the individual was given the vaccine, increasing by 1 each tick.  This is compared against the seroconversion-time, selected from a gamma-distribution.  
  seroconversion-time          ;; The randomly chosen gamma-distribution value for how long it will take the individual to seroconvert.
  
  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   
  set seroconversion-alpha (average-seroconversion-period * ticks-per-day)^ 2 / (seroconversion-standard-deviation * ticks-per-day)^ 2    
  set seroconversion-lambda (average-seroconversion-period * ticks-per-day) / (seroconversion-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 vaccination? false      
    set seroconverted? false  
     
    set shape "person"
    
    set total-contacts 0
    
   set number-infectious-vector [ 1 ]   ;; The number-infectious-vector vector is initiallized.  
   set number-vaccinated 0
   set infection-possible true
   assign-color
  ]
end 

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

;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
;;;; Go Procedure ;;;;

to go
  if not infection-possible                                                                                 ;; The simulation ends when no individuals are infected (exposed or infectious).  
    [ stop ]                                                                                 
  
  ask turtles                                                                        
    [ move ]
  
  if ticks / ( ticks-per-day ) = day-of-first-infection                                                     ;; After a given delay, one susceptible individual becomes infectious.  
      [ first-infection ] 
    
  ask turtles with [ infectious? ]                                                                          ;; Infectious individuals might expose susceptible and not seroconverted neighbors.  If infectious individuals have been infectious for infectious-time ticks, they will recover. 
    [ expose-neighbors 
      chance-of-recovery ] 
    
  if ticks / ( ticks-per-day ) mod 1 = 0                                                                    ;; Once each day, some susceptible and exposed individuals are given the vaccine.  
    [ ask turtles with [ ( susceptible? or exposed? ) and not seroconverted? ]
      [ chance-of-receiving-vaccine ] 
    ]
      
  ask turtles with [ vaccination? and susceptible? and not seroconverted? ]                                 ;; If vaccinated and susceptible individuals were given an effective vaccine and have been in the exposed class for seroconversion-time ticks, they will seroconvert. 
    [ chance-of-seroconverting ]
     
  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 ]

  if all? turtles [ susceptible? or recovered? ] and ticks / ticks-per-day > day-of-first-infection         ;; The simulation ends when no individuals are infected (exposed or infectious).  
    [ set infection-possible false ]  

  compute-maximum-infectious  
  
  tick
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 first-infection
  ifelse any? turtles with [ susceptible? and not seroconverted? ]   
    [ 
      ask one-of turtles with [ susceptible? and not seroconverted? ]
      [ 
          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                                                          
        ]   
    ]
   [ set infection-possible false ]
end 

to expose-neighbors
  ask other turtles in-radius 1 with [ susceptible? and not seroconverted? ]               ;; Susceptible individuals who come into contact with an infectious individual will become infected with probability transmission-chance.
    [ 
      if random-float 100 < 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 chance-of-receiving-vaccine                                                             ;; Once each day, each susceptible and exposed individual has a chance of receiving the vaccine.  Some vaccinations will be effective.                                                      
  if random-float 100 < daily-vaccination-chance    
    [
      set number-vaccinated number-vaccinated + 1           
      set vaccination? true                                        
      set shape "default"                                
      ifelse random-float 100 < vaccine-efficacy                     
      [
        set seroconversion-time random-gamma seroconversion-alpha seroconversion-lambda    ;; The vaccine is effective and a newly vaccinated individual selects a seroconversion-time from the gamma-distribution and its seroconversion-length is set to 0.
        set seroconversion-length 0 
      ]
      [
        set seroconversion-time 1000000                                                    ;; The vaccine is not effective and a newly vaccinated individual has a seroconversion-time much longer than the length of an outbreak.  
        set seroconversion-length 0 
      ]
    ]
end     

to chance-of-seroconverting                                                                ;; When a susceptible and vaccinated individual has been vaccinated longer than its seroconversion-time, it will seroconvert.  
 set seroconversion-length seroconversion-length + 1
   if seroconversion-length > seroconversion-time                                     
   [                                                                                  
     set seroconverted? true
   ]
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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There is only one version of this model, created about 2 years ago by Anna Mummert.

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