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MIDAS Model Profiles

Table of Contents

 

1     Model Profiles. 5

2     City Model – Eubanks. 5

2.1     Spatial Characteristics. 5

2.2     Social Networks. 5

2.3     Transmission Process. 6

2.4     Intervention Strategies: Definition and Caveats. 6

2.5     Seeding Assumptions. 7

2.6     Calibration Assumptions. 7

2.7     Model Outputs and Discussion.. 7

3     Southeast Asia – Longini/Nizam/Xu.. 8

3.1     Spatial Characteristics. 8

3.2     Social Networks. 9

3.3     Transmission Process. 9

3.4     Intervention Strategies: Definition and Caveats. 10

3.5     Seeding Assumptions. 11

3.6     Calibration Assumptions. 11

3.7     Model Outputs and Discussion.. 12

4     Southeast Asia – Ferguson/Burke. 13

4.1     Spatial Characteristics. 13

4.2     Social Networks. 14

4.3     Transmission Process. 14

4.4     Intervention Strategies: Definition and Caveats. 14

4.5     Seeding Assumptions. 15

4.6     Calibration Assumptions. 15

4.7     Model Outputs and Discussion.. 15

4.8     Model Caveats. 16

5     United States – Germann/Longini 16

5.1     Spatial Characteristics. 16

5.2     Social Networks. 16

5.3     Transmission Process. 17

5.4     Intervention Strategies: Definition and Caveats. 17

5.5     Seeding Assumptions. 18

5.6     Calibration Assumptions. 18

5.7     Model Outputs and Discussion.. 18

6     United States – Ferguson/Burke. 19

6.1     Spatial Characteristics. 19

6.2     Social Networks. 20

6.3     Transmission Process. 20

6.4     Intervention Strategies Definition and Caveats. 21

6.5     Seeding Assumptions. 22

6.6     Calibration Assumptions. 22

6.7     Model Outputs and Discussion.. 22

7     Great Britain – Ferguson/Burke. 24

7.1     Spatial Characteristics. 25

7.2     Social Networks. 25

7.3     Transmission Process. 25

7.4     Intervention Strategies: Definition and Caveats. 25

7.5     Seeding Assumptions. 25

7.6     Calibration Assumptions. 26

7.7     Model Outputs and Discussion.. 26

 

 


 

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.

 

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.

·         PV - pre vaccinate a proportion of the susceptible population using a poorly matched vaccine.

·         Q – quarantine a percentage of susceptible persons to restrict movements to households and neighborhood.

Specific Strategies

1.       No intervention

2.       70% Q

3.       80% TAP

4.       90% GTAP

5.       80% TAP & 50% PV

6.       80% TAP & 70% PV

7.       80% TAP & 50% PV & 70% Q

8.       80% TAP & 70% PV & 70% Q

9.       80% TAP & 70% Q

 

Antiviral treatment assumptions:

·         infectiousness reduction = 62%;

·         Susceptible reduction = 30%;

·         Symptomatic reduction = 60%.

 

Vaccines:

·         Poorly matched vaccine:

o        susceptibility reduction = 30%

o        infectiousness = 30%

o        probability of becoming a clinical case is reduced by 50%.

 

TAP cases are treated one day after detection. Each person to be treated is given a single course of Oseltamivir - 5 days of treatment. Each person to be prophylaxed is given a single course of Oseltamivir for 10 days.

 

Pre vaccination takes place before epidemic and immunity is developed

Quarantine – contacts in neighborhoods and households are doubled.

 

All interventions carried out in the localities as triggered:

·         80% targeted antiviral prophylaxis (TAP)

·         90% geographically targeted antiviral prophylaxis (GTAP)

 

Interventions represent localized household and household cluster quarantine.  Quarantine is lifted when there are no more local cases.

3.5         Seeding Assumptions

For calibration to historical attack rates, influenza was introduced by randomly assigning 12 initial infectives. The emergence of a new influenza strain was simulated by introducing a single randomly assigned infective.

3.6         Calibration Assumptions

The model was calibrated with a target overall illness attack rate of 33% and to a pattern that fell between two extremes.

 

At one extreme, children would have a much higher illness attack rate than adults, which was the pattern observed during the 1957-1958 influenza pandemic in the United States.

 

At the other extreme, all age groups would have roughly the same illness attack rates, the pattern observed during the 1968-1969 epidemic.

Attack Rates

 

 

57-58

model

68-69

Young Children

35%

32%

34%

Older Children

62%

46%

35%

Adults

24%

29%

33%

Overall

33%

33%

34%

 

Sources:

·         L. R. Elveback et al., Am. J. Epidemiol. 103, 152 (1976).

·         W. S. Jordan, Am. Rev. Res. Dis. 83, 29 (1961).

·         I. M. Longini, E. Ackerman, L. R. Elveback, Math.

·         Biosci. 38, 141 (1978).

·         L. E. Davis, G. C. Caldwell, R. E. Lynch, R. E. Bailey,

·         Am. J. Epidemiol. 92, 240 (1970).

·         R. G. Sharrar, Bull. World Health Org. 41, 361 (1969).

3.7         Model Outputs and Discussion

The following results are recorded by the Longini SE Asia model:

·          tf1.out: contains one record for each simulation.  In each record, the following variables are recorded:

1.  illness attack rate in young children (age < 5)

2.  illness attack rate in older children (age >=5)

3.  illness attack rate in adults

4.  illness attack rate overall

5.  # of people migrating out of the area during the epidemic day outbreak was recognized

6.  number of courses of antivirals used

7.  number of people ill at start of intervention

 

The SAS program tf1.sas reads tf1.out and averages the attack rate results over all simulations recorded in tf1.out.

 

·         tf2.out: contains individual level information (i.e. 500,000 records) per simulation.  The following information in appears for each person:

1.       simulation number

2.       id number

3.       age group

4.       initial infective status: 0=not initially infected, 1=initially infected

5.       illness status: 0 not ill, 1 ill

6.       day ill: day illness began

7.       inf_f: infected in family? 0=no, 1=yes

8.       inf_n: infected by neighbor? 0=no, 1=yes

9.       inf_d: infected in daycare or small play group?

10.    inf_s: infected in school?

11.    inf_w: infected in work group?

12.    inf_sg: infected in social group?

13.    inf_hp: infected by hospital patient?

 

The SAS program tf2.sas reads tf2.out and averages the results over all simulations.

 

·         ill.out: contains information on the number of people who become ill      in each simulation, on each day, in each subpopulation.  The following information is recorded in each record:

1.       simulation number

2.       day

3.       number ill in subpopulation 1

4.       number ill in subpopulation 2

5.       number ill in subpopuation 36

·         inf.out: contains information on the number of people who are infected: in each simulation, on each day, in each subpopulation.  The following information is recorded in each record:

1.       simulation number

2.       day

3.       number infected in subpopulation 1

4.       number infected in subpopulation 2

5.       number infected in subpopulation 36

 

·         dayill.out: contains details on who became ill on each day. The following information is recorded in each record:

1.       simulation number

2.       day

3.       id numbers of people who become ill on this day (space delimited)

·         dayrecover.out: contains detailed on who recovered on each day.

1.       The following information is recorded in each record:

2.       simulation number

3.       day

4.       id numbers of people who recovered on this day (space delimited)

4         Southeast Asia – Ferguson/Burke

The Ferguson/Burke Southeast Asia Model was created to assess the feasibility of containing flu at its source. It was supported by NIGMS, INSERM Department of Community Medicine, The University of Hong Kong, Bureau of Epidemiology, Department of Diseases Control and the Ministry of Public Health, Thailand.

 

It has been published in Nature in 2005:

·         Ferguson NM, Cummings DAT, Cauchemez S, et al., “Strategies for containing an emerging influenza pandemic in Southeast Asia”, Nature. 2005;437:209-214

4.1         Spatial Characteristics

The Ferguson/Burke SE Asia Model covers Thailand and a 100 km buffer zone around the land borders of Thailand. No special structure population was distributed according to 2003 LandScan data source.

 

Sources for the data are:

·         LandScan- population density.

·         National Statistical Office Thailand

·         Population and Labor Statistics and National Statistical Office Thailand

·         Population Census 2000 – household size and age structure

 

These data use a population of 85,000 synthetic agents.

4.2         Social Networks

The model uses households, schools, workplaces, community sites as network elements with the following mixing:

·         Children assigned to schools by age.

·         The average school size was 175, 420, and 750 pupils for primary, elementary and secondary schools respectively, but no constraints are imposed on any given school.

·         School location imputed.

·         Number of employees per workplace is modeled.

·         Workers are assigned to conform to travel survey data.

 

There were a number of data sources used to create and calibrate population activities. These include:

·         National Statistical Office Thailand,

·         Population and Labor Statistics

·         National Statistical Office Thailand, Education and Public Health Statistics.

·         Ministry of Education Thailand, Class size data for Thai schools (schools Size)

·         Survey of migration in Thailand 1995 contained information about travel to schools and/or workplaces and random travel.

4.3         Transmission Process

The model makes the following natural history assumptions:

 

New estimates of the incubation period and period of infectiousness were derived.

·         Latent (non-infectious) period: Weibull distribution (2.21,1.10 + .5 day offset) that resulted in a mean of 1.48 days and SD .47 days.

·         Modeling of infectiousness (sickness): infectiousness modeled as varying through time according to a lognormal functional form, but truncated at 7 days post onset of infectiousness.

·         Generation Time (average time between infection of an index case and infection of the secondary cases caused by the index case) = 2.6 days

·         Proportion of infections resulting in symptoms severe enough for health-care to be sought (or for detection via clinical surveillance) = 50%

·         Earliest possible report of symptoms: .5 days after end of latent period. No weekend or seasonal affects are represented.

·         33% of transmission was assumed to occur in households, 33% in schools and workplaces, and 34% in the wider community. The proportion of household transmission was estimated from epidemiological data from household studies of seasonal influenza transmission.

 

Overall transmission levels were varied to give basic reproduction number (R0) values in the range 1.1 to 2. R0 was empirically calculated from model output.

4.4         Intervention Strategies: Definition and Caveats

Intervention strategies include:

·         TAP - prophylaxing individuals in the same household, school, or workplace.

·         GTAP – prophylaxing individuals in a geographic area with a cap that restricts treatment to 10k to 50k nearest people within 5k or 10km of a diagnosed case.

·         School closures

·         Antiviral treatment - infectiousness reduction = 60%, Susceptible reduction = 30%. 

·         Area quarantine zones – movements in and out of an area are restricted

 

Intervention assumptions include:

·         Antiviral stockpile – 50K to 150K

·         Detection occurs after 20 (40) severe (symptomatic cases) usually 14 days.

·         TAP begins 1(2) days after detection. 90% of household members and schoolmates and fellow workers treated.

·         GTAP covers 90% of population, 1 or 2 days after detection.

·         School closures increase household and random contacts by 50 to 100%

4.5         Seeding Assumptions

Simulations were seeded with a single infection in the most rural third of the population, assuming that rural populations are most likely to be exposed to the avian virus.

4.6         Calibration Assumptions

Proportion of transmissions in:

·         households = 33%

·         schools and workplaces=34%

·         community=33%

 

Ratio of schools versus workplace transmissions coefficients = 2

4.7         Model Outputs and Discussion

The following variables are recorded by the Ferguson/Burke SE Asia Model:

 

1.       Time

2.       Susceptibles Prevalence

3.       Latent infecteds Prevalence

4.       Incubating Infecteds Prevalence

5.       Recoverds Prevalence

6.       Deaths Prevalence (not used)

7.       Latent infecteds Incidence

8.       Recoverds Incidence

9.       Deaths Incidence (not used)

10.    The average the average (across non-extinct model runs) of the cumulative number of treatment courses of antivirals used.

11.    The maximum number of treatment courses used by that time point in any run.

12.    the root-mean-square maximum radius (measured from the source case) of the distance spread of the epidemic in km, with the average being across runs

13.    The maximum distance spread (across runs)

14.    Susceptibles Prevalence (Variance)

15.    Infecteds  Prevalence (Variance)

16.    Recoverds Prevalence (Variance)

17.    Deaths Prevalence (Variance) – Not used

18.    Latent infecteds incidence (Variance)

19.    Recoverds incidence (Variance)

4.8         Model Caveats

A number of key criteria must be met for a high probability of success:

1.       Rapid identification of the original case cluster,

2.       Rapid, sensitive case detection and delivery of treatment to targeted groups, preferably within 48 h of a case arising,

3.       Effective delivery of treatment to a high proportion of the targeted population, preferably .90%,

4.       Sufficient stockpiles of drug, preferably 3 million or more courses of oseltamivir,

5.       Population cooperation with the containment strategy and, in particular, any social distance measures introduced,

6.       International cooperation on policy development, epidemic surveillance and control strategy implementation.

 

Antiviral resistance represents a currently unquantifiable challenge to a prophylaxis-based containment strategy.

 

If a transmissible resistant strain did emerge during implementation of a containment policy, it would be essential for prophylaxis to cease, lest the wild-type virus be eliminated and the world be left with a pandemic of resistant virus.

5         United States – Germann/Longini

The Germann/Longini US Model was created to assess strategies for mitigating pandemic influenza in the continental US. It represents collaboration between DHHS and Los Alamos.

 

It was published in the Proceedings of the National Academy of Science in 2006:

·         Germann TC, Kadau K, Longini IM Jr, Macken CA, “Mitigation strategies for pandemic influenza in the United States”, Proc Natl Acad Sci . 2006;103:5935-5940.

5.1         Spatial Characteristics

The Germann/Longini US Model covers the Continental United States. Structured communities of 2,000 persons are stochastically generated by the age distribution and household size. The population of each Census tract is rounded to 2,000 persons and each Census tract is populated with the approximate number of 2,000-person communities.

 

A family is a group of up to seven persons living together with one or two adults. They are grouped into clusters of 4 households. Households are grouped into groups of 4 neighborhoods.

 

A neighborhood contains about 500 persons.

 

The model employs the 2000 US Census data used by the Transims application to generate a synthetic population; i.e. 2000 US Census data:  TIGER data, Summary File 3 (SF3) data, Public Use Micro data Sample (PUMS).

 

These data use a population of 281,000 synthetic agents.

5.2         Social Networks

The model uses households, day-care, playgroups, schools, workplaces, neighborhood clusters and neighborhoods as network elements with the following mixing:

·         Pupils were assigned to synthetic schools (average sizes 79 to 155 pupils); 93% attend school.

·         Workers were assigned to synthetic work groups of about 20 people each.

·         Pre schools children are assigned to a neighborhood daycare center (n= 14) or a neighborhood playgroup (n=4).

 

There were a number of data sources used in the model:

·         STP64 commuter data, for short-to-medium distance travel.

·         Airline travel survey data (1995) from the Department of Transportation, Bureau of Transportation Statistics. These data were used to define long term travel (business and vacation)

5.3         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

·         Infectious period is 4.1 days

·         % symptomatic is 67

·         Rate of infectiousness is fixed

·         No weekend or seasonal affects are represented.

5.4         Intervention Strategies: Definition and Caveats

Strategies consist of one or more of (1) targeted antiviral prophylaxis (TAP) – individuals and most of their close partners, (2) mass vaccination – random or children targeted, (3) closure of schools, pre-schools and play groups, and (4) social distancing (SD): travel restrictions, quarantine programs voluntary changes in social behavior.

 

The following is a list of intervention examined by the model:

1.       Unlimited TAP

2.       Dynamic vaccination (low efficacy)

3.       Child first vaccination (low-efficacy)

4.       Dynamic vaccination (high-efficacy)

5.       Child first vaccination (high - efficacy)

6.       School closure

7.       Travel restrictions

8.       Local social distancing

9.       Combination of 7 and 8 above

10.    Combination of 1, 6 and 8 above

11.    Combination of 3, 6, 7 and 8 above

12.    Combination of 1, 3, 6, 7 and 8 above

13.    Combination of 3, 6, 7 and 8 above

 

Antiviral treatment reduces infectiousness by 62%, susceptible by 30%, clinical sickness by 60%.

 

Well matched vaccine reduces susceptibility by 70%, infectiousness by 50%; the probability of becoming a clinical case is reduced by 80%.

 

Poorly matched vaccine reduces susceptibility by 30%, infectiousness by 30%; the probability of becoming a clinical case is reduced by 50%.

 

The model assumes that:

·         TAP is triggered 7 days after pandemic alert, 20M courses of antiviral available. TAP administered after 1st asymptomatic case in household is detected. 60% are detected, 0% false positives. 95% of all household members treated. 60% - 95% of daycare or pre-schoolers treated if index case a member of that group.

·         SD is triggered by 10,000 symptomatic cases. Contact rates halved for all networks except households, which are doubled.

·         10 M doses of low-efficacy vaccine will be available per week. Intervention lasts 25 weeks; response is immediate.

·         School closure starts 7 or 14 days after pandemic detection, and remains for the duration of a pandemic.

·         Long-distance travel is reduced by 90% (or SOM says 99%)

·         Antiviral treatment reduces infectious period by 1 day.

5.5         Seeding Assumptions

The 14 largest international airports act as gateways. Each day a random number (N) of infections is introduced into a random Census tract near one of the 14 airports. N is proportional to the number of arriving daily passengers (5/10,000)  

5.6         Calibration Assumptions

Contact probabilities were calibrated against age-specific attack rates and among different mixing groups.

 

Data Source: Longini I.M., M.E., Halloran, A. Nizam, Y Yang, Am J Epidemiol. (2004)

5.7         Model Outputs and Discussion

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

1.       Attack rates (%)

2.       Attack rates Standard Deviation

3.       Antiviral courses per 1000

4.       Antiviral courses Standard Deviation

5.       Time to peak (day)

6.       Duration (day)

7.       ILI attack rate (%)

8.       Average absenteeism due to case withdrawal or quarantine (%)

9.       Average absenteeism due to place closure (%)

10.    % attack rate in 0-5 age group

11.    % attack rate in 5-15 age group

12.    % attack rate in 15-20 age group

13.    % attack rate in 20-60 age group

14.    % attack rate in 60-85 age group

15.    % of infections in household

16.    % of infections in daycare

17.    % of infections in playgroup

18.    % of infections in school

19.    % of infections in workplace

20.    % of infections in neighborhood cluster

21.    % of infections in neighborhood

 

Epidemic threshold is recognized after the report of the 10,000th case.

·         Number long-range trips reduced to X% of normal.

·         Once imposed, maintained throughout pandemic outbreak.

 

Containment assumptions involve:

·         7 days post-alert; or

·         10 days post-alert; or

·         14 days post-alert;

Vaccine:

·         10M doses/week for 25 weeks of low-efficacy vaccine, first protection coincides with introduction of virus;

·         10% of normal travel

 

It is important to rapidly estimate key parameters of pandemic strain, including:

·         Pathogenicity, virulence, natural history, case fatality parameters

·         Transmissibility parameters

o        R0

o        Serial interval

o        Secondary attack rates (age-specific)

o        Age-specific overall attack rates

·         Need estimation for inter-pandemic influenza

o        Test interventions

o        Household transmission studies

6         United States – Ferguson/Burke

The Ferguson/Burke US Model was created to assess strategies for mitigating pandemic influenza in the Continental United Sates. It represents collaboration with DHHS and was published in Nature in 2006:

·         Ferguson NM, Cummings DAT, Fraser C, et al., “Strategies for mitigating an influenza pandemic”, Nature advance online publication. 2006;442:448-452.

6.1         Spatial Characteristics

The Ferguson/Burke US Model covers the Continental United States.

 

No special structure population was distributed according to 2003 LandScan data source. Household size and age distribution generated from US census data and with no regional patterns.

 

Data sources include LandScan 2003 with regular grid size (from Oakridge) and the US-Bureau Census Households by size and Interim population projections.

 

These data use a population of 300,000,000 synthetic agents.

6.2         Social Networks

The model uses households, schools, workplaces, hotels, community sites as network elements with the following mixing:

 

·         Schools locations and sizes are modeled as specified in national file dataset on all US public schools.

·         Workplace size distribution was matched to available US data.

·         Assignment of child to school is age-specific, and chosen to match census data.

·         The assignment of workers to work sites uses commuting data, household location and available workplace capacity to assign workers to workplaces. The age-specific proportion of the population in work generated by the model matches available US Census data.

·         Commuter data are obtainable from the STP64 dataset, which has a Census tract resolution, (65,000 Census tracts in the US). Data on the centroid locations of the Census tracts were used to construct distributions of the distance traveled to work.

·         Air travelers are assigned from an OD study and mix in hotels, 3 million rooms occupied per night, 30,000 hotels with average occupancy of 100 rooms. Hotels are distributed according to population density. Destination airport selected to match OD data. 50% of hotel occupants are local, randomly picked. Capacity restrictions operate i.e. travelers do not stay at hotels that are at capacity.

·         There are 571 airports in a simulation of  the US with the following assumptions:

o        460,000 passengers per day.

o        Modeling people moving from airport to airport is simple.

o        Several assumptions about who goes to which airport, where they go and what they do when they arrive. However, results not sensitive to these assumptions.

·         Workgroups are modeled as a set of colleagues that an individual interacts with closely: 75% of an individual’s contacts were within-a group and 25% with individuals at random from the entire population of the school or workplace.

 

Data Sources include:

·         US school census, National Center for Ed. Statistics national file on public schools containing grades, capacity and addresses.

·         STP64, US Bureau of the census 2004.

·         Airline traffic OD study (2005)

6.3         Transmission Process

The model makes the following natural history assumptions; see natural history parameters for SE Asia Ferguson/Burke model:

·         30% of transmission was assumed to occur in households, 37% in schools and workplaces, and 33% in the wider community. The proportion of household transmission was estimated from epidemiological data from household studies of seasonal influenza transmission.

o        A single place type was assumed for schools, but schools had age-specific capacities determined by the NCES data source. School classes were modeled within schools. Individuals were randomly assigned to school classes (of a size determined from data) or workgroups (assumed to have an average size of 10). Workgroups are viewed as the set of work colleagues an individual mostly closely interacts with.  75% of an individual’s contacts were assumed to be within-group, and 25% between-group.

·         Community transmission is modeled as localized random mixing in the community: the risk of transmission depends on a power-law function of the distance between the households of the infected and susceptible individuals being considered.  The parameters of the power-law distribution are chosen to match available data on the distribution of journey distances, the underying hypothesis being that the distance distribution of community contacts will be determined by the distance distribution of travel distances.

·         To model the mixing of air travelers with people local to an area, it was assumed that 50% of the occupants of hotels were local. Individuals were picked at random from the local community, with a distance weighting given by the workplace selection kernel. Residency times in hotels for air travelers and local travelers were derived from data on long-distance travel in the US. People in hotels were assumed to have no household, school or workplace contacts while away. Transmission in hotels was assumed to occur at random among all occupants, at the same rate as workplace transmission.

·         No weekend or seasonal affects are represented

·         Overall transmission levels were varied to give basic reproduction number (R0) values in the range 1.1 to 2, with most results being presented for the 2 values of 1.7 and 2. R0=1.7 represents the ‘best guess’ of the transmissibility of pandemic influenza based on 1918 and 1957 data, while 2.0 represents a worst case (derived from 1918 data). R0 was empirically calculated from model output.

 

Data sources include:

·         National Center for Educational Statistics (2004).

·         US Bureau of Transportation Statistics (2005)

6.4         Intervention Strategies Definition and Caveats

Intervention strategies include:

·         Border controls (applied at rates of 90%, 99% and 99.9%).

·         Area quarantine – a system of zones is drawn around households containing an infected. Travel across zones is restricted.

·         Blanket travel restrictions - all travel further than (20 km or 50 km) from home is reduced.

·         Antiviral treatment - infectiousness reduction = 60%, Susceptible reduction = 30%, clinical sickness reduction = 65. 

·         Case isolation – reduces household, workplace/school and community contact rates by 90%.

·         Household quarantine – applies to all people in a household with a clinical case and reduces contacts by an unknown amount. 

 

Well matched vaccine reduces susceptibility by 70%, infectiousness by 50%; the probability of becoming a clinical case is reduced by 50%.

 

Poorly matched vaccine reduces susceptibility reduction by 30%, infectiousness by 30%; the probability of becoming a clinical case is reduced by 50%.

 

A total of 30 combination strategies were applied to 2 R0 assumptions, i.e. 60 different experiments were run that investigate treatment effectiveness.

 

Intervention assumptions include:

·         Case detection = 90% of all cases

·         Border controls (applied at rates of 90%, 99% and 99.9%) are applied 30 days into epidemic.

·         Travel across zones is restricted by (75%, 90% and 100%).

·         Antiviral treatment is applied 1 day delay before treatment, 100% of detected cases are treated:

o        in households - 100% treatment

o        in schools - 90% of classmates

o        in workplaces - 90% of fellow workers

·         Case isolation effect occurs 1 day after report of symptoms and lasts 7 days.

·         Household quarantine sees 75% compliance for 14 days, beginning 1 day after index case is reported.

·         Well matched vaccine protection start 2 weeks after inoculation

·         Poorly matched vaccine coverage for this option is 90%

6.5         Seeding Assumptions

Infection seeding is based on a global SEIR model that supplies external travelers to the US at a rate that is based on an external epidemic that has an R0 = 1.6. This model was used to calculate incidence of infection through time based on 73 million trips per year (Non-US nationals plus US travelers returning from overseas travel).Non-US nationals select destinations proportional to population size.

 

One third (1/3) of the trips are US returnees.

 

Trips occur at locations according to population density.

 

Returning travelers are expected to have more random destinations than foreign visitors.

6.6         Calibration Assumptions

Proportion of transmission in:

·         households is 30%

·         schools and workplaces is 37%.

·         community is 33%

 

Ratio of schools versus workplace transmissions coefficients is 2

6.7         Model Outputs and Discussion

The following list represents values generated by the model:

 

1.       Scenario

2.       Generic/workplace social distancing

3.       Treat all ILI as flu

4.       School closure type

5.       Other controls

6.       Threshold for closure and social distancing

7.       R0

8.       Proportion of infections becoming cases (%)

9.       Cumulative attack rate by day 220 of global epidemic (~day 180 of US epidemic) (%)

10.    Peak attack rate (%)

11.    Antiviral usage (%)

12.    Cumulative non-flu ILI attack rate (%)

13.    Time to peak (days)

14.    Duration of epidemic (days)

15.    Average absenteeism due to case withdrawal or quarantine (%)

16.    Average absenteeism due to place closure (%)

17.    % of infections due to seeding

18.    % of infections in households

19.    % of infections in schools

20.    % of infections in workplaces

21.    % of infections in community

22.    % of infections in 0-5 age band

23.    % of infections in 5-15 age band

24.    % of infections in 15-20 age band

25.    % of infections in 20-60 age band

26.    % of infections in  60-85 age band

 

Clinical impact of treatment:

·         Assume 50% of infections become ‘cases’ – i.e. have ILI (arbitrary), independent of age, and 90% of these can be detected.

·         These are 2-fold more infectious than non-ILI-generating infections (assumption based on data from Hayden et al. & Cauchemez et al.).

·         Uninfected individual on prophylaxis has 30% reduction in susceptibility.

·         Infected person has 60% reduction in infectiousness.

·         Additionally, a treated infected person has 65% reduction in chance of becoming a ‘case’.

·         Assume matched pandemic vaccine reduces susceptibility by 70%.

·         Vaccinated people who still get infected have infectiousness reduced by 30%, and are 50% less likely to be a ‘case’.

 

Antiviral treatment:

·         Assume 90% of cases treated on same day symptoms start.

 

Need for rapid treatment:

·         Infectiousness peaks soon after symptoms start for human flu.

·         Hence early treatment can reduce transmission substantially (as well as having best clinical effect).

·         48h delay to treat reduces impact of treatment on transmission substantially (as well as clinical benefit).

 

Antiviral Treatment assumes 90% of cases are treated on day after symptoms start, and 95% of other household members are prophylaxed.

 

School Closure:

·         Assume 90% of cases are treated on day after symptoms start.

·         After the first case in a school, it is closed the next day for 21 days, then closes again if there are further cases after 21 days. 10% of workplaces assumed to close similarly.

·         Key uncertainty: proportion of transmission in schools/workplaces (here assumed to be 1/3).

·         People home from school have a 50% increase in household contact rates, and a 25% increase in community contact rates.

 

Household prophylaxis & school closure combines next day treatment with household prophylaxis and school closure policy.

 

Case Isolation:

·         Assume 90% of cases are treated on day after symptoms start, and then isolated with 90% effectiveness.

 

Household Quarantine:

·         Assume 90% of cases are treated on day after symptoms start.

 

Socially targeted prophylaxis:

·         As household prophylaxis, but with 90% prophylaxis of school classes and workgroups of cases

 

Mass Vaccination:

·         Assume 90% of cases are treated on day after symptoms start.

o        Assume vaccine starts to be manufactured on the day 0, 30, 60 or 90 of the US epidemic.

o        Doses for 1% or 2% of population are manufactured per day (i.e. 45 or 90 days to 90% coverage).

o        Vaccine takes 21 days to confer protection.

 

Pre-vaccination of targeted groups use a stockpile of trial vaccine before or soon after first US cases occur in new pandemic. Matched pandemic is assumed to be available from 2 months into pandemic (1% coverage per day). Also, there is the assumption that a vaccine is partial match (50% reduction in susceptibility), and is effective before substantial numbers of cases have accumulated.

 

Key sensitivities in general:

·         Transmissibility (=R0).

·         Proportion of transmission occurring in different contexts (home, school, workplace, community).

·         Proportion symptomatic (50%) and reporting to healthcare (90% of 50%).

·         Behavior of symptomatics (assume 2x more infectious, likely to stay home from school or work).

·         Natural history of infection – have assumed ‘human flu like’. If ‘avian-like’ (i.e. more severe and extended pathogenesis), more options available.

·         Details of population structure, movements etc not very important – would only be so if real control was feasible.

·         If viral shedding (and infectiousness) is constant for 7 days, treatment only policies (or better still, isolation) have a much enhanced impact.

7         Great Britain – Ferguson/Burke

The Ferguson/Burke Great Britain Model was created to assess strategies for mitigating pandemic influenza on the island of Great Britain. It represents collaboration with DHHS.

7.1         Spatial Characteristics

The Ferguson Burke GB Model covers the island of Great Britain.

 

No special structure population was distributed according to 2003 LandScan data source. Household size and age distribution were generated from UK census data and with no regional patterns.

 

Data sources include:

·         LandScan - 2003 with regular grid size.

·         UK estimated resident population by age and sex and percentage of households by size.

 

These data represent 58.1 million synthetic agents.

7.2         Social Networks

The model uses Households, Schools, Workplaces, Hotels, Community sites as its network elements with the following mixing:

·         Data on the average size of primary (218 pupils in 2004) and secondary schools (949 pupils in 2004) and on average class sizes and staff-student ratios were used to generate a synthetic population of schools distributed in space with a density proportional to local population density. Proportions of each age group assumed to be in school or work matched to UK census data. Children were allocated to schools using a free selection algorithm. Staff-student ratios were used to determine the proportion of adults to schools rather than other workplaces.

·         Data on origin-destination flows for travel-to-work derived from 1991 Census were used. The resolution of these data was ward level, there being approximately 10,000 wards in GB. Data on the centroid locations of the wards was used to construct distributions of the distance traveled to work. Workplace size distribution assumed to be same as for US model.

 

Data sources include:

·         Department of Education and Skills. Statistics of Education: Schools in England (HMSO, 2004).

·         UK public for transport (2003).

·         Office of National Statistics UK (2005).

7.3         Transmission Process

The model makes the following natural history assumption

·         As US Ferguson/Burke model (Section 6), except air travel not included, and UK travel data used for commuting kernel and community transmission.

7.4         Intervention Strategies: Definition and Caveats

See Section 6.4.

7.5         Seeding Assumptions

Infection seeding is based on a global SEIR model that supplies external travelers to the GB at a rate that is based on an external epidemic that has an R0 = 1.6. This model was used to calculate incidence on infection through time based on 92 million trips per year (Non-US nationals plus US travelers returning from overseas travel).

 

Approximately 1/3 of inbound travel is due to residents returning home from overseas trips. Trips occur at locations according to population density.

 

Returning travelers are expected to have more random destinations than foreign visitors.

7.6         Calibration Assumptions

See Section 6.6.

7.7         Model Outputs and Discussion

See Section 6.7.