MODEL PROFILES

 1         Model Profiles

Modeling is a complex endeavor, and often it is very difficult to reconcile results from different models. In many cases, journals do not allow enough space to completely describe model structure and assumptions. To aid in this process of model description and comparison, a set of model profiles - one for each MIDAS model - has been developed.

 

Model profiles are standardized descriptions of simulation models developed to aid comparison of models and their results. Each MIDAS model has a profile that describes modeling details, assumptions data sources and implementation issues.

 

Note: This document will be updated periodically. The most current version is now posted on this site. We recommend you let your interests guide you through this document, using the navigation tree as a general guide to the content available. a#_Toc162077243

 

The intent of this document is to provide the interested reader with insight into ongoing research. Model parameters, structure, and results contained herein should be considered representative but preliminary in nature. We encourage interested readers to contact the contributors for further information.

2         City Model - Eubanks

The Eubanks City Model is based on the Virginia Bioinformatics Institute�s version of the open source tool EpiSims. EpiSims was created to assess the feasibility of examining an infectious disease in a medium and large size American City. Model development has been supported by DHHS, the Homeland Security Council and others. EpiSims has been used to assess the spread of flu in Chicago and Portland, as well as smallpox in Portland. The material below is based on the flu - Portland scenario.

2.1         Spatial Characteristics

This version of EpiSims covers the Portland metropolitan area and assumes the population is distributed according to the 2000 Census. The travel topography of the study region defines the spatial area represented by the model.

 

The Transims applications used 2000 US Census data to generate a synthetic population. These data included TIGER data, Summary File 3 (SF3) data and Public Use Microdata Sample (PUMS) to identify 1.6 million synthetic agents.

2.2         Social Networks

The model uses households, schools, workplaces, colleges, shopping places, community activities as network elements with the following mixing behaviors:

 

 

    •          Shopping, recreational and "other" buildings are based on the activity-based travel plans of the individuals in the population. These buildings have rooms, with maximum occupancies that are specified as a data input. The number of buildings for each activity type is determined by the counts of how many people arrive at each location throughout the day to perform the various activities at that location. 
  •          Schools are modeled at the level of synthetic classroom. Mixing occurs within the classroom and between classrooms. Teachers come into contact with students. Whether or not a child goes to school is determined from the activity data.
  •          Workplace data are contained in the activity sets produced by the Transims activity generator. People always arrive at the same room of the same work building, and there is some mixing between rooms. 
  •          Shopping locations consist of several large rooms per building.
  •          Families depart from, and return to the same home building during each day of the simulation.

     

 

An activity or travel survey of Portland residents and population mixes according to an activity/travel survey provided a source for social network data.

 

There were about 30 data sources used to create and calibrate population activities. These include:

 

  •          Land use and tax lot information 
  •          Transportation demand studies (e.g. Traffic counts), 
  •          Trip purpose surveys (e.g., stopping people driving across a bridge to find out the purpose of their trip) and
  •          Activity surveys.

     

2.3         Transmission Process

The model makes the following natural history assumptions:

 

  •          Onset time between an infection and illness is 3.2 days 
  •          Latency period is 1.2 days
  •          Incubation period is 1.7 days
  •          Symptomatic period is 3.5 days
  •          % symptomatic - 67
  •          Rate of infectiousness is fixed

     

Based on a survey of daily behavior patterns, agents move through a "real" network of (for example) breakfast patterns, travel patterns, work/school patterns, shopping patterns, etc. Every time agents come into contact with other agents and one of the agents is infected with flu, the likelihood of a transmission is recorded. If transmission occurs, the disease status of the infected individual is updated and influences future model actions.

 

For this study, transmission only depended on the age of the susceptible person (because susceptibility was either uniform across ages or doubled for kids and seniors - that's one of the experimental parameters). No weekend or seasonal affects are represented.

2.4         Intervention Strategies: Definition and Caveats

Intervention strategies include:

 

  •          Antiviral treatment to reduce susceptibility and infectivity:

     

    o                         Prophylax (to reduce morbidity) versus treatment (to reduce mortality & morbidity).

    o                         Option 1: all available anti-virals are used for prophylaxis.

    o                         Option2: Half of the antiviral stockpile is used for antiviral treatment the other half for prevention.

     

  •          Vaccination:

     

    o                         Generic H5N1 vaccine (poorly matched): vaccinate according to age.

    o                         Method 1: allocate vaccine to persons age < 18 or persons age > 65.

    o                         Method 2: allocate to persons between the ages of 18 to 65 only.

     

  •          Strain-specific vaccine � Availability

     

    o                         Method 1: 26,000 doses administered per week

    o                         Method 2: 130,000 doses administered per week.

     

  •          Efficacy of vaccines (masks) for protecting susceptibles:

     

    o                         Method 1: 10% protection

    o                         Method 2: 60% protection

 

In addition to the infected person, some households will curtail all activities outside the home. That fraction can be influenced by parametric specification.

 

A fraction of symptomatic adults withdraw to the home after the first day of symptoms appear. Two rates were analyzed 30% and 60%. Also, a fraction of symptomatic adults withdraw to the home after the second day of symptoms. Two rates (30% and 60%) were assumed� in this scenario.. Finally, the fraction of households that curtail all activities outside the home, such as by observing a snow day (close school, work, shops, etc) is also assumed.

 

 

  •          Assumption 1: 25% curtailment

     

     

  •          Assumption 2: 75% curtailment.

     

 

Schools are either all open or all closed without secondary responses by parents etc. Closing transit does not produce a very large effect. Transit is allowed to operate normally (uncalibrated) or not at all.

 

Mask assessment was not used in the HHS study.

 

The model assumes

 

  •          There are always prophylax households of symptomatics.

     

     

  •          There are vaccinations two weeks before start of simulation.

     

     

  •          The available courses of treatment are to distribute vaccine uniformly by population; there is an H5N1 vaccine stockpile for 20 million people and that strain-specific vaccine is produced at a rate of 4 million to 20 million doses per week.

     

 

The Fraction of households curtailing activities is 0.25 (0.75), mixing on mass transit vehicles is normal (none), mixing at school locations is normal (none)

2.5         Seeding Assumptions

Two methods were used to seed the epidemic model:

 

  •          Method 1: 10 adults were chosen at random and 1 more was selected per day.

     

     

  •          Method 2: 1,000 adults were chosen at random and 10 more w selected per day.

     

2.6         Calibration Assumptions

The person-person transmission rates were calibrated to an R0 in the range roughly [1.5 from 2.0]. The overall attack rate was calibrated to 30%.

2.7         Model Outputs and Discussion

The following results are recorded by the Episims City Model:

 

Widely applied social distancing measures can control an outbreak. Implementation details are crucial, vary by locality, and must be part of plans. However, these measures are delaying tactics and likely to cause social disruption comparable to pandemic.

 

Antivirals can control an outbreak in plausible scenarios. Their effectiveness is sensitive to uncontrollable properties of the disease such as its transmissibility and development of drug resistance. A "portfolio" combining different controls reduces the exposure to uncertainties in any one area.

 

The following is a list of values generated by the model:

 

1.       Proportion of infections becoming cases

2.       Attack rates (%)

3.       Peak attack rate (%)

4.       Antiviral courses per 1000

5.       5Time to peak (day)

6.       % attack rate in 0-5 age group

7.       % attack rate in 5-15 age group

8.       % attack rate in 15-20 age group

9.       % attack rate in 20-60 age group

10.    % attack rate in� 60-85 age group

11.    % of infections in 0-5 age group

12.    % of infections in 5-15 age group

13.    % of infections in 15-20 age group

14.    % of infections in 20-60 age group

15.    % of infections in� 60-85 age group

16.    % of infections at home

17.    % of infections at work

18.    % of infections when shopping

19.    % of infections at schools

20.    % of infections at college

21.    % of infections when "other"

3         Southeast Asia - Longini/Nizam/Xu

The Southeast Asia- Longini/Nizam/Xu model was created to assess the feasibility of containing flu at its source (somewhere in Asia). It represents collaboration between the NIGMS and the Ministry of Public Health, Thailand.

 

An application of the model was published in Science in 2005:

  • Longini IM Jr., Nizam A, Xu S, et al., - Containing pandemic influenza at the source, Science. 2005;309:1083-1087.

3.1         Spatial Characteristics

The SE Asia - Longini model covers a 5,625 km rural area of Thailand and assumes 36 homogeneous quads or squares that measure 12.5 km x 12.5 km. Each square or locality contains 14,000 people and 28 villages for each locality, 138 households and 500 persons per village

 

Sources for the data are:

 

  •          LandScan - population data from the National Statistical Office Thailand. Population and housing census 2000 matches rural Thailand.

     

     

  •          Nang Rong study - for demographic data and social network data

     

 

These data use a population of 500,000 synthetic agents.

3.2         Social Networks

The model uses schools, workplaces, households, household clusters, community (markets, shops, temples), neighborhoods and regional hospitals with the following mixing:

 

 

  •          All people can mix in households;

     

     

  •          Children mix in schools according to age groups.

     

     

  •          Adults mix at workplace according to a distance function.

     

     

  •          All schools are synthetic. Children 5-10 attend schools of average size 117; children of ages 10-14 attend secondary schools with average size 95. Children ages 15-17 assigned to schools of average size 69. Children 5-10 assigned to local elementary schools. Two villages share each elementary school. Children 11-14 assigned to secondary schools and 17% of children 11-14 do not attend school. Children 15-17 are assigned to upper secondary schools but 42% of children 15-17 do not attend and are in the workforce. Assignments are made using a gravity model. Workers interact with 21 persons in a work group. Assignment is based on a gravity model. 82% of adults assigned to a work group.

     

     

  •          For community mixing, adults interact randomly with two social networks of average size 100, contacts are casual and untraceable.

     

     

  •          One 40-bed hospital serves 36 localities. One flu holding facility with 100 beds is assigned to each locality. When hospitals are full, patients go to holding facility, otherwise they stay at home. There are 40 hospital staff. Each person in the population has a daily probability of .001 of going to the hospital for a non flu reason.

     

 

Social networking data are based on the Nang Rong study and Thailand health profile.

3.3         Transmission Process

The model makes the following natural history assumptions:

 

  •          Onset time between an infection and illness is 3.2 days

     

     

  •          Latency period is 1.2 days

     

     

  •          Incubation period is 1.7 days

     

     

  •          Symptomatic period is 3.5 days

     

     

  •          % symptomatic is 67

     

     

  •          Rate of infectiousness is fixed

     

 

The transmission process:

 

  •          c daily adequate contact probability, c(n-1) average mixing group degree

     

     

  •          x transmission probability given adequate contact

     

     

  •          y relative susceptibility

     

     

  •          p=cxy overall transmission probability

     

 

Daily infection probability applies to an untreated susceptible person on day t

 

  •          Infection model based on a sequence of Bernoulli trials

     

     

  •          Escape probability: Q(t)=(1 -p1)I1(t) (1 -p2)I2(t) (1 -p3)I3(t) . . . . . . .

     

     

  •          Infection probability: P(t)=1 - Q(t)

     

     

  •          Antiviral efficacy of reducing susceptibility to infection: - AVES=0.30 (from literature)

     

     

  •          Antiviral efficacy of reducing infectiousness to others: AVEI=0.62, [0.31, 1.00] 95% CI

     

     

  •          Antiviral efficacy of reducing illness with infection: AVESD=0.86, [0.70, 1.00] 95% CI

     

     

  •          Daily contact probabilities by mixing group

     

    o        Within Small playgroups=0.35

    o        Within Large playgroups=0.25

    o        Within Elementary school, Middle school and High school� children=0.062

    o        Within Family - child to child=0.60

    o        Within Family - child to adult=0.30

    o        Within Family - adult to child=� 0.30

    o        Within Family - adult to adult=� 0.40

    o        Within Neighborhood - child to child=0.15

    o        Within Neighborhood - child to adult=0.08

    o        Within Neighborhood - adult to child=0.08

    o        Within Neighborhood - adult to adult=0.10

    o        Within Hospital - worker-worker=0.01250

    o        Within Hospital - patient-worker=0.01000

    o        Within Hospital - patient-visitor=0.01000

    o        Within Hospital non flu ward � everyone-everyone=0.00250

    o        Within workplaces � everyone-everyone=0.115

    o        Within all other social groups � everyone-pre-schoolers=0.0024

    o        Within all other social groups � everyone-schoolers=0.00255

    o        Within all other social groups � everyone-adults=0.0048

    o        No weekend or seasonal effects are represented.

 

Source:

 

  •          Anti viral data from Welliver, et al. JAMA (2001);

     

     

  •          Hayden, et al. JID (2004);

     

     

  •          analysis by Yang, Longini, Halloran (2004)

     

3.4         Intervention Strategies: Definition and Caveats

General Intervention strategies include:

 

  •          TAP- treat index case and a fixed % of persons in close-contact groups (households, pre-schools, schools and workplaces.

     

     

  •          GTAP- treat a fixed % of persons in a locality.