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Overview
Agents in FRED represent individuals in a population living in a specific geographic region. For example, many of the initial studies with FRED model the population of Allegheny County surrounding Pittsburgh, Pennsylvania. The model of the population of Allegheny County includes 1,242,755 agents. Each agent has demographic information (e.g., age, date-of-birth, sex), health information (e.g., current health status, date of infection, level of symptoms, infectiousness, susceptibility), locations for daily activities (household, neighborhood, and possibly school or workplaces), and health-related behaviors (e.g., probability of getting a vaccine or staying home when sick). During each simulated day, agents interact with the other agents who share the same daily activity locations. If an infectious agent interacts with a susceptible agent, there is a possibility of transmitting a condition from the infected agent to the susceptible agent. FRED simulates the population of agents during a specified period of time, ranging from several months to several years, and tracks the spread of condition among the population. Since each infection event is recorded, it is possible to analyze the course of an infection through the population and to evaluate several possible control measures.
The population input files specify the sex, race, age, marital status, school status, and work status of each agent. By default, these demographic features remain constant during a simulation run.
FRED optionally supports population dynamics including aging, births and deaths. If population dynamics is enabled, then an agent's age increases on each birthday, and females of child-bearing age may become pregnant using age-specific maternity rates. Upon becoming pregnant, the agent is assigned a due-date based on a Gaussian distribution with a mean of 280 days and a standard deviation of 7 days. When the due-date arrives, the mother gives birth to a new agent who is assigned a random sex and is assigned to the same household as the mother. Deaths occur based on age- and sex-specific mortality rates. When an agent dies, it is removed from the population. Maternity and mortality rates are based on US averages for 2010, but may be overrideen by user-defined values.
Each agent maintains a list of its current health conditions and infections, if any. Each condition follows a condition-specific natural history (e.g., incubation and latent periods, infectious period, symptomatic period, as well as level of infectiousness and symptoms) as specified via input parameters. Each infection is also associated with the date of infection, the identity of the infector agent, the place of infection, and other details. An agent's health information also includes immunity status, treatment status, susceptibility, current symptom levels, and how many others have been infected by this agent.
Each agent follows a daily pattern of interactions with groups of other agents. All interactions in FRED occur in a specific place. The types of places include households, neighborhoods, schools, classrooms, workplaces, offices, and hospitals. Classrooms are small mixing groups with a given school. Offices are small mixing groups with a workplace. Each agent maintains list of daily places to visit, at most one for each of the above types. Agent may may not participate in every activity. For example, working adults may not have a defined school.
Neighborhoods are defined on a grid with 1 km square cells. The agent's home neighborhood is the neighborhood patch in which its household is located. An agent may visit another neighborhood in the community during a given day. The decision about where to spend the neighborhood activity period is made independently each day, using a gravity model to define inter-neighborhood travel patterns.
If an agent is infectious, then any location the agent visits during that day is considered an active location. Susceptible agents can only become infected at an active location, so interactions among agents at non-active locations need not be simulated.
Schools are closed on weekends and during scheduled summer holidays. Schools may also be closed due to school closure policies. Students do not attend their school when the school is closed.
Similarly, most workers do not attend their workplaces on weekends. However, some workers are designated as weekend workers, and they continue to attend their workplaces on weekends.
To reflect weekend schedules of schools and workplaces, the number of neighborhood contacts is increased by 50% on weekends.
Agents in FRED can be given a number of health-related behaviors. Each behavior involves a decision on the willingness of the agent to perform the behavior. The current set of behaviors includes:
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Stay home when sick: If an adult is symptomatic, is that person willing to stay home? If so, the agent withdraws to the household, does not interact with other in the neighborhood, at work or at school. The agent also does not begin new overnight travel.
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Keep child home when sick: If a child is symptomatic, is the child's adult decision-maker willing to have the child withdraw to the household. In this case, the same restrictions on contact apply as in the adult "stay at home when sick" behavior.
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Accept vaccine: Is an adult willing to accept a vaccine, if one is available?
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Accept vaccine for child: This is the adult's willingness to have a child vaccinated.
Other behaviors may include: wearing a face mask; taking anti-viral prophylaxis; staying home when well; keeping children home when well; avoiding travel; avoiding neighborhood contacts; hand-washing; and others.
The FRED synthetic population includes information giving the relationship of each member of the household to the Householder (typically, the owner of the house or the head of the household.) This information is used to assign an adult in the household as the responsible decision-maker for the health-related behaviors of each child in the household. The rules for selecting the adult decision-maker for each child are as follows:
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If the Householder is the parent (natural parent, adoptive parent, step-parent) of the child, then the Householder is designated the child's decision-maker.
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If the Householder is the grandparent of the child and there is an adult in the householder who is a child of the Householder, then the first such adult is designated as the decision-maker for the child. Note that the household relationship data does not provide enough information to determine whether such an adult is actually the parent of the child in question.
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If the Householder is the grandparent of the child and no plausible adult parent is present in the household, then the Householder is designated the decision-maker for the child.
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Otherwise, a random adult in the household is designated as the decision-maker for the child.
The rules above permit multiple decision-makers per household. No preference is made on the basis of sex or age, other than that each decision-maker is an adult (i.e., at least 18 years old.)
How real people make health decisions is an active area of research without an obvious consensus theory. Indeed, it seems likely that different people use different methods to come to decisions about health-related behavior. FRED agents can apply a variety of strategies to determine their willingness to adopt a given behavior. Each agent may revisit its willingness to perform the given behavior. Thus each strategy specification includes a frequency parameter that determines how often agents make decisions about their willingness to perform the behavior.
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Refuse: Agent is never willing to perform the given behavior.
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Accept: Agent is always willing to perform the given behavior.
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Flip Behavior: Agent is assigned a fixed probability p of being willing to perform the given behavior. The agent revisits its willingness to perform the behavior according to the frequency parameter.
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Imitate Prevalence: The agent is assigned an initial probability p of being willing to perform the given behavior. The agent revisits its willingness to perform the behavior according to the frequency parameter. When reconsidering the decision, the agent estimates the prevalence of willingness among the agents in its social networks: household, neighborhood, school and workplace. The estimate is a weighted average of the actual prevalence in each group. Given the weighted estimate, the agent adjusts its probability p toward the perceived prevalence. For example, if the agent perceives that the prevalence of willingness is 0.75, then it adjusts its own probability to be closer to 0.75.
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Imitate Consensus: This strategy is similar to the Imitate Prevalence except that if the weighted estimate of prevalence exceeds a threshold, the agent adjusts its probability p toward 1; otherwise the agent adjusts its probability toward 0. For example, if the agent's threshold is 0.5, then if the agent perceives that the majority of its associates are willing to perform the behavior then the agent becomes more likely to accept the behavior; otherwise the agent becomes more likely to refuse the behavior.
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Imitate by Count: This strategy is similar to the Imitate Consensus except that if the weighted number of nearby agents exceeds a threshold, the agent adjusts its probability p toward 1; otherwise the agents adjusts its probability toward 0. For example, if the agent's threshold is 3.0, then if the agent perceives that at least three of its associates is willing to perform the behavior then the agent becomes more likely to accept the behavior; otherwise the agent becomes more likely to refuse the behavior.
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Health Belief Model: According to the Health Belief Model, people make health behavior decisions based on several specific considerations: susceptibility, severity, benefits, and barriers.
a. Perceived Susceptibility refers to the person's estimate of how likely he or she is to become adversely affected by the condition or condition;
b. Perceived Severity refers to the level of adverse consequences that are perceived to be likely if the person become affected;
c. Perceived Benefits refers to the estimated protective effects of the behavior;
d. Perceived Barriers refers to the conditions that may prevent the agent from performing the behavior.
These constructs are clearly specific to the particular health behavior under consideration, so including an HBM strategy for a particular behavior in FRED requires customized programming. However, once the perceptions are computed, they can be combined into a decision rule using formulas developed in (Durham, 2010). These formulas have been implemented in the FRED Behavior module, and are controlled by run-time parameters.
Each agent is assigned a strategy independently for each behavior defined for that agent.
For each behavior in FRED, the user may specify the fraction of the population using each strategy for that behavior. For example, it might be desirable to investigate the effect of varying the fraction of the population using the Accept, Refuse, and Imitate Consensus strategies. The user can specify a given distribution, for example, 20% of the population adopts the Accept strategy, 30% adopts the Refuse strategy, and 50% adopt the Imitate Consensus strategy for a given behavior. The share of the population can be specified separately for each behavior.
All infections in FRED are transmitted from one agent to another in some particular place. The types of places in FRED include: Households, Neighborhoods, School, Classrooms, Workplaces and Offices. The synthetic population files specify the households, school and workplaces in the modeled region. Neighborhoods, classrooms, and office are created by FRED using the methods described below.
Neighborhoods are defined on a grid with 1 km square cells. The agent's home neighborhood is the cell in which its household is located. However, an agent may visit another neighborhood in the community during a given day.
Classrooms are small mixing groups with a given school. Classrooms are defined by dividing up all the students who attend a given school into separate age groups. Each age group is divided into classroom groups of up to a maximum numbe of students. A student interacts with the students assigned to the same classroom for the entire school year. A student also interacts (at a separate rate) with all the students attending the same school.
Offices are small mixing groups with a given workplace. Offices are defined by dividing up all the workers in a given workplace groups of up to 50 workers. A worker interacts with the other workers in the same office, and, with a separate rate, with all workers in the same workplace.
School and classrooms are closed on weekends, during scheduled summer breaks, and possibly due to school closure policies.
FRED supports multiple conditions circulating in the same population. Each condition has separate parameters specifying natural history (e.g., latent period, infectious period, symptomatic period, case fatality rate, etc.) and its transmission paremeters.
Each condition has an associated Epidemic object that keeps track of population level statistics associated with the condition, such as the number of agents that are susceptible, exposed, infectious and recovered. The Epidemic object prints out the daily reports to the output file.
The core phenomenon of an epidemic in FRED is the spread of an infection from one agent to another in a particular place. Each type of place represents a distinct environment for the spread of infection. Each type of place is characterized by two sets of numeric parameters:
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the number of contacts per infectious person per day, and
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the probability that a contact transmits an infection
The number of contacts per day for each type of place is a tunable parameter, and is set through the process described in the Calibration Section.
The transmission probability for a give place type generally depends on the age of the infectious person and the susceptible person. These are specified as vector input parameters.
FRED is parameterized for a default pandemic influenza strain following the process described in (Cooley P, Brown S, Cajka J, Chasteen B, Ganapathi L, Grefenstette J, Hollingsworth CR, Lee BY, Levine B, Wheaton WD, Wagener DK. The Role of Subway Travel in an Influenza Epidemic: A New York City Simulation. J Urban Health. 2011 Aug 9. [Epub ahead of print] PubMed PMID: 21826584.) Paraphrasing the Supplementary Material from (Cooley et al, 2011):
The pandemic was assumed to have the age-dependent attack rate pattern of the historical 1957-8 "Asian" influenza A (H2N2), see Longini et al. Accordingly, we calibrated our model using the Ferguson et al. approach from historical (1957-58, 1968-69) influenza pandemics. We specifically used the 30-70 rule developed by Ferguson et al. in which 70% of all transmission occurred outside the household: 33% in the general community and 37% in schools and workplaces.
Following (Cooley et al, 2011), we adopted that additional requirement that transmission rates in schools are double those in workplaces. Calibrating the model involved targeting an epidemic with a 33% attack rate (AR) consistent with the age specific parameters derived from the 1957-58 pandemic. Daily contact rates were treated as endogenous parameters and were interpreted as the daily contact rates that reproduced a pandemic with a 33% AR in a population with no acquired immunity and satisfied the 30-70 rule. Therefore, our estimated contact patterns produced an epidemic designed to be similar in transmissibility to the 1957-58 epidemic with an AR of 33% and a basic reproductive rate (R0) of approximately 1.4.
By default, the contact rates for classrooms are double those for the school in general. Likewise, the contact rates for offices are double those for workplaces in general. These heuristic are based on the idea that individuals sustain more contacts within their smaller mixing groups at school and at work.
As in (Cooley et al, 2011) we assumed that 50% of sick individual stay at home and do not interact with anyone outside of the household. Note that our default school absentee rate is generally lower than other models (e.g., Ferguson et al. use a 90% absentee rate). Additionally, we assumed that all community contacts increase by 50% on weekends.
Calibration to the 30-70 target criteria was impossible unless within household contacts were treated differently than other locations. Following (Cooley at al, 2011), we assumed that each pair of agents within a household make contact each day with a specified probability. This probability is tuned as part of the calibration step to achieve the 30-70 target distribution.
FRED provides a fairly robust capability for simulating the use of vaccines during a pandemic. Multiple vaccines can be simulated simultaneously, with differing administration schedules and target groups, and with different efficacies. Each vaccine can also have multiple doses and be restricted by age. It is also possible to model varied vaccines schedules by day. Prioritization by age groups, or by ACIP recommendation is available with the capability to vaccinate only the priority group. Currently, each vaccine can only be applied to one condition.
Vaccines in FRED are currently modeled as so-called "all or nothing" vaccines. Each vaccine is given an age-specific efficacy and efficacy delay. When an agent takes a vaccine, there is a random draw to determine whether the vaccine will be efficacious for that agent. If it is not, then the vaccine has no effect until another vaccine or dose is administered. If the vaccine dose is efficacious, then the agent will become immune to the condition after the specified efficacy delay. As in real life, the agent has no knowledge as to whether their dose of vaccine was efficacious, and so if they are exposed after a failed vaccine or during the delay period, they may get sick from the condition.
FRED currently implements mass vaccination strategies. At the beginning of the simulation, a set of queues is set up based on prioritization of the agents. These queues are then randomized and as vaccines are put into the system, agents can choose whether or not to accept a vaccine. To determine this decision, the simulation can use a straight coverage probability, or a more complex behavioral model. Heads of households can make decisions for younger members.
FRED provides the ability to simulate the use of antivirals. Use of multiple antivirals can be modeled simultaneously. Modifiable antiviral characteristics include the length of antiviral treatment, the reduction in infectivity and susceptibility due to treatment, the efficacy of the antiviral, the amount of antiviral initially and currently available, and the start date for administration. The stock of an antiviral may be increased daily. Viral evolution can change the efficacy of an antiviral. Antivirals can modify the infectivity, susceptibility, and symptomaticity of an agent. Antivirals have distribution policies that determine to whom they are given. An antiviral may be designated as being used for prophylaxis.
FRED includes two levels of school closure policies: global and
individual. A global school closure policy affects all schools in the
simulation at once. An individual school closure policy allows each
school to close indepently. There are two triggers for the global school
closure policy. First, all schools can be closed on a specified
simulation day. Second, all schools can be closed if the population
attack rate exceeds a specified school_closure_threshold. With either
trigger, school closure is delayed by a number of days indicated by the
parameter school_closure_delay. Schools reopen after a number of days
indicated by the parameter school_closure_duration.
If the individual school closure policy is selected
(school_closure_policy = individual), then the parameters for the
attack rate used as threshold (school_closure_threshold), delay
(school_closure_delay), and duration (school_closure_duration) are
used are applied to each school independently. Schools may close again
if the school attack rate exceeds the threshold.
The default is no school closure policy:
school_closure_policy = none
School are always closed on weekends. All schools also close for the
summer if the parameter school_summer_schedule is set. In that case,
schools are closed between the dates specified by parameters
school_summer_start and school_summer_end, inclusive.
© 2012-2015 [Public Health Dynamics Laboratory] (http://www.phdl.pitt.edu "PHDL website"), University of Pittsburgh