Modeling Bird/Human Interaction with Avian Influenza

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Modeling Bird/Human Interaction with Avian
Influenza
Mathematical Modeling
Nicole Rogerson and Theresa Holtz North Edgecombe
High School Craven Early College
2008
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Whats the Problem?

• Tracking the Avian Influenza virus
• Trends between people and bird populations

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Outline

• What is avian influenza?
• Describing our models
• Results using trial and error
• Variations in our model
• A quick review
• In the future

http//www.topnews.in/health/files/Bird_Exam.jpg
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What is Avian Influenza (H5N1)?

• Influenza A
• Respiratory
• Coughing, congestion, sore throat, muscle aches,
  fatigue, fever
• Spreads through birds the same way the flu
  spreads through people, except for coughing
• It is a potential pandemic

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http//ec.europa.eu/health/ph_threats/com/Influenz
a/images/influenza.jpg
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How did we get our models?
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How did we get our models?
susceptibles recovered infectives
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How did we get our models?
infected birds infected humans recovered humans
recovered birds
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What do these symbols mean?

• transmittivity constant determines rate
  of infection for birds
• rate of recovery for birds
• atransmittivity constant determines rate of
• infection for humans
• b rate of recovery for humans

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Assumptions and possible constants in our models

• Assume that in every country that had reported a
  bird flu case, all people are susceptible

1,720,083,064
1,571,237,542
1,470,187,016
147,555,041
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Assumptions and possible constants in our models

• Constants are susceptible birds
• Numbers are high
• They dont vary much over time

11,270,536
9,319,991
1,064,694
677,362
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Infected People from 2004-2007
http//upload.wikimedia.org/wikipedia/en/7/7f/H5n1
_spread_28with_regression29.png
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People Infected Data
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Birds Infected 2004-2007
1,188,752
1,107,307
115,893
42,866
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Birds Infected-Data
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Fit Data to Model
Assume s(t) constant s0
Find a and b to fit infected bird population.
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Determining Parameters

• Decreasing the rate at which birds get infected
• The graph goes up and turns right
• birds infected over time is smaller

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Increasing Transmission Rate - Bird Population -

• Increasing the rate at which birds get infected
• line went right then straight up
• the birds infected over time shot up into
  unrealistic numbers

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Recovery Rate

• Changing the rate of recovery of the infected
  bird population
• line goes out into a half parabola
• Makes a wide curve

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Results-Bird Population
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Fit Human Population Data
Find a and b to fit infected bird population.
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Changing Transmission Rate

• Changing the rate of infection of the human
  population
• doesnt really change much even if totally
  opposite values are put in
• Only moves the line farther away from the y-axis

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Increasing Recovery Rate

• Increasing the rate of recovery of the humans
  makes the line go straighter

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Decreasing Recovery Rate

• Decreasing the recovery rate of humans curves the
  line

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Results Human Population
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Further Improvements

• Birds

• Humans

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New Model Logistic Term
Birds
Humans
ci2 limited growth term
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Quadratic Fit p(t) to Data
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Exponential Fit i(t)i0ekt
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Modified Models
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Our Findings

• Birds arent tracked as carefully as humans when
  it comes to Avian Influenza.
• Birds should be tracked as well as humans because
  they are the ones carrying the virus, not humans.
• There wasnt enough information about the birds,
  so we didnt have a lot of data to work with

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To the future!

• Look at the Spanish flu.
• Compare results to Avian influenza H5N1
• Look at other strains of Avian Influenza (H7N2,
  H7N3,H7N7,H9N2)

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A Quick Review

• What Avian Influenza H5N1 is.
• How we got and tested our models.
• What we found out.

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Bibliography

• Siegel, Marc. Bird Flu Everything you need to
  know about the next pandemic . New Jersey John
  Wiley Sons, Inc, 2006.
• "Bird Flu Everything you need to know about the
  next pandemic ." Oie. 09/07/2008. World
  Organization for Animal Health. 8 Jul 2008
  lthttp//www.oie.int/downld/AVIAN20INFLUENZA/A2004
  _AI.phpgt.
• "Cumulative Number of Confirmed Human Cases of
  Avian Influenza A/(H5N1) Reported to WHO."
  Epidemic and Pandemic Alert and Response (EPR).
  19 June 2008. World Health Organization . 6 Jul
  2008 lthttp//www.who.int/csr/disease/avian_influen
  za/country/cases_table_2008_06_19/en/index.htmlgt.
• "Global Cumulative number of human cases of
  avian influenza A/(H5N1)." EINet. 6Jul 2008
  lthttp//depts.washington.edu/einet/?aprintArticle
  print5054gt.
• "Index of /worldfacts/countries." AirNinja . H
  Brothers Inc. 1 Jul 2008 lthttp//www.airninja.com/
  worldfacts/countries/gt.
• "Central Intelligence Agency ." The World
  Factbook. CIA. 6 Jul 2008 lthttps//www.cia.gov/lib
  rary/publications/the-world-factbook/index.htmlgt.

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Acknowledgments

• SVSM Staff
• Dr. Herman
• Mr. Glasier
• Parents (both families)
• Mrs. Moser
• Mrs. Land