School Closure Model

Overview

This model studies the effects of school closures in Jefferson County, PA. The main.fred file includes three components:

  • Influenza condition

  • school.fred: a condition for group agents to close the school according to case numbers in their school or county as well as normally scheduled holiday closure dates. This condition also keeps track of students whose schools are closed.

  • parameters.fred : a file written into by the METHODS script to modify the school closure policies and other variables.

Normal Closures

The schools are given a school schedule that closes the schools during summer, winter, and spring break. There are states for each break: WinterBreak, SpringBreak, andSummerBreak. In these states, school administrators (represented by group agents) close their schools and wait until the end of the break period. They pass into these states from the CheckCalendar state:

state CheckCalendar {
    wait(0)
    if (date_range(Dec-20,Jan-02)) then next(WinterBreak)
    if (date_range(Mar-10,Mar-15)) then next(SpringBreak)
    if (date_range(Jun-15,Aug-25)) then next(SummerBreak)
    default(Open)
}

Group agents go to the break states by checking the current date with date_range(). The group agents only pass into this check state if their school is not already affected by flu closures. No flu closures will take place if school_closure_policy is set equal to NO_CLOSURE.

School Closure due to Flu

The schools are also setup to actively check the number of cases of flu either in their school or in their county and close schools if the number passes a threshold set by one of the variables: local_closure_trigger or global_closure_trigger. After deciding to close due to the flu, the admin goes to the Close state, and the school remains closed for a time period set by the variable days_closed.

Global Flu Closure

The GLOBAL_CLOSURE, LOCAL_CLOSURE, and NO_CLOSURE variables are set to arbitrary but unique integers to get around the inability to assign strings to variables. The global closure option is selected by setting school_closure_policy = GLOBAL_CLOSURE. This variable passes group agents from the CheckEpidemic state in the SCHOOL condition to the CheckGlobalEpidemic state:

state CheckGlobalEpidemic {
    wait(0)
    if (global_closure_trigger <= current_count(INF.Is)) then next(Close)
    default(CheckCalendar)
}

This state checks the county flu count against the global threshold, local_closure_trigger. If the threshold is reached, then all group agents go to Close state.

Local Flu Closure

The local closure option is selected by setting school_closure_policy = LOCAL_CLOSURE. This variable passes group agents from the CheckEpidemic state in the SCHOOL condition to the CheckLocalEpidemic state:

state CheckLocalEpidemic {
    wait(0)
    if (local_closure_trigger <= current_count(INF.Is, School)) then next(Close)
    default(CheckCalendar)
}

In this state, each admin checks if the number of infected agents in their own school is greater than the threshold set by local_closure_trigger. If the number is greater or equal, then the admin goes to the Close state and closes the school, otherwise they pass to the check_calendar state.

Student Tracking

The StudentSchoolOpen and StudentSchoolOpen states are included in the SCHOOL condition to keep track of how many students have their school closed/open over the course of time. Students are filtered into StudentSchoolOpen from the Start state with the conditional if (is_member(School) & age < 18). The students then switch between the two states by checking if their school has been closed by an admin using the is_temporarily_closed(<group>) predicate. ##Results

Plotting Flu Cases

The following plots show the effectiveness of the different policies in limiting the number of total and daily infections as a percent of the county population.

tot

inc

Plotting School Closures

The plots below show the number of schools closed and number of students out of school over time. Because the threshold for school closure is the same regardless of school size, the larger schools are more likely to close under the local closure policy. This results in a higher percentage of students out of school than percentage of schools closed for the local policy.

closed

students

Modifying Closure Variables

FRED variables are modified in the METHODS script for this model, which overwrites various combinations the school_closure_policy, days_closed, global_closure_trigger, and local_closure_trigger variables. For each combination of interest, the changes are written into the parameters.fred file and then fred_job is called to execute the model with the modified parameters. This produces a range of results as captured in the following figures.

In each figure, the modified variable values are shown in the legend for the figure. The other variables not represented in a figure use the following default values:

  • global_closure_trigger = 1000

  • local_closure_trigger = 20

  • days_closed = 28

Changing the global_closure_trigger Variable

global_trigs_tot

global_trigs_new

Changing the local_closure_trigger Variable

local_trigs_tot

local_trigs_new

Changing the days_closed Variable Under Global Closure

global_days_closed_tot

global_days_closed_new

Changing the days_closed Variable Under Local Closure

local_days_closed_tot

local_days_closed_new