# SEIR-Model-Isolation

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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. ] 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. isolation? ;; If true, the individual is in isolation. 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. total-not-isolated-contacts ;; A count of all contacts with individuals not in isolation, for individuals that are not themselves in isolation. ] ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; ;;;; 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 isolation? false set shape "person" set total-contacts 0 set total-not-isolated-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 ] 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 ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; ;;;; Go Procedure ;;;; to go if all? turtles [ susceptible? or recovered? ] ;; The simulation ends when no individuals are infected (exposed or infectious). [ stop ] ask turtles with [ not isolation? ] ;; Individuals in isolation freeze; all other individuals move on each tick. [ move ] ask turtles with [ infectious? and not isolation? ] ;; Infectious and non-isolated individuals might expose susceptible neighbors. [ expose-neighbors ] ask turtles with [ infectious? ] ;; If infectious individuals have been infectious for infectious-time ticks, they will recover. [ chance-of-recovery ] ask turtles with [ infectious? and not isolation? ] ;; Infectious and non-isolated individuals might isolate. [ chance-of-isolating ] ask turtles with [ isolation? and not infectious? ] ;; Individuals in isolation that recover, exit isolation. [ exit-isolation ] 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 end ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; ;;;; 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. Not-isolated-contacts are between two individuals both not in isolation. set total-contacts total-contacts + count other turtles in-radius 1 if not isolation? [ set total-not-isolated-contacts total-not-isolated-contacts + count other turtles in-radius 1 with [ not isolation? ] ] 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 < 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-isolating ;; Once each day, an infectious individual will isolate with probability isolation-chance. if ticks / ticks-per-day mod 1 = 0 [ if random-float 100 < daily-isolation-chance [ set isolation? true set pcolor gray ] ] end to exit-isolation ;; After an isolated individual recovers, they leave the isolation class. if recovered? [ set isolation? false set pcolor black ] 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 ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;

There is only one version of this model, created about 4 years ago by Anna Mummert.

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Anna Mummert

## 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 3 years ago

Daniel Zamzow

## Problems with this model (Question)

We have been running this model in our Micro class and it crashes quite often. The program simulation will stop after 5-10 days whenever the Daily Isolation Chance is adjusted.

## Posted 10 months ago

Anna Mummert

## RE: Problems with this model

When the Daily Isolation Chance is higher than the default, the simulation will end after 5-10 days more often. This is expected. When the Daily Isolation Chance is higher it means that infectious individuals are less likely to spread the disease. Therefore the outbreak will end sooner. For example, when the Daily Isolation Chance is 25%, three out of ten simulations looked like a "real outbreak", long (average 72 days) with a well defined peak of infection; the other seven ended on average after 8 days. At 50%, zero of ten simulations looked like a "real outbreak"; all ten ended quickly, on average after 5.75 days. (Simulations run with all other parameters at their default values.) This model shows the importance of Isolation as a method to end / control the spread of infectious diseases like influenza.

## Posted 10 months ago