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Modeling Bird/Human Interaction with Avian Influenza

Modeling Bird/Human Interaction with Avian Influenza. Mathematical Modeling. Nicole Rogerson and Theresa Holtz North Edgecombe High School Craven Early College. 2008. What’s the Problem?. Tracking the Avian Influenza virus Trends between people and bird populations.

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Modeling Bird/Human Interaction with Avian Influenza

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  1. Modeling Bird/Human Interaction with Avian Influenza Mathematical Modeling Nicole Rogerson and Theresa Holtz North Edgecombe High School Craven Early College 2008

  2. What’s the Problem? • Tracking the Avian Influenza virus • Trends between people and bird populations http://tk.files.storage.msn.com/x1pUr2osLO3XWjESyfPMmOH5SY3GtDQ1HGa1nrdHHfAaarZzRWEYkF5x_ueI40CZC329LSFFV2x0Q7pISR9bmXRBJsok8mdQQSLlcWtVyiZEPgB8hzb5YLgZEII6pPG0kAFQKnwPgXBGNQ

  3. 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

  4. 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

  5. http://ec.europa.eu/health/ph_threats/com/Influenza/images/influenza.jpghttp://ec.europa.eu/health/ph_threats/com/Influenza/images/influenza.jpg

  6. How did we get our models?

  7. How did we get our models? susceptibles recovered infectives

  8. How did we get our models? infected birds infected humans recovered humans recovered birds

  9. What do these symbols mean? • : transmittivity constant; determines rate of infection for birds • :rate of recovery for birds • a=transmittivity constant; determines rate of infection for humans • b= rate of recovery for humans

  10. Assumptions and possible constants in our models • Assume that in every country that had reported a bird flu case, all people are susceptible

  11. Assumptions and possible constants in our models • Constants are susceptible birds • Numbers are high • They don’t vary much over time 11,270,536 9,319,991 1,064,694 677,362

  12. Infected People from 2004-2007 http://upload.wikimedia.org/wikipedia/en/7/7f/H5n1_spread_%28with_regression%29.png

  13. People Infected – Data

  14. Birds Infected 2004-2007 1,188,752 1,107,307 115,893 42,866

  15. Birds Infected-Data

  16. Fit Data to Model Assume s(t) = constant = s0 Find a and b to fit infected bird population.

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

  18. 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

  19. Recovery Rate • Changing the rate of recovery of the infected bird population: • line goes out into a half parabola • Makes a wide curve

  20. Results-Bird Population

  21. Fit Human Population Data Find a and b to fit infected bird population.

  22. Changing Transmission Rate • Changing the rate of infection of the human population: • doesn’t really change much even if totally opposite values are put in • Only moves the line farther away from the y-axis

  23. Increasing Recovery Rate • Increasing the rate of recovery of the humans makes the line go straighter

  24. Decreasing Recovery Rate • Decreasing the recovery rate of humans curves the line

  25. Results – Human Population

  26. Birds Humans Further Improvements

  27. New Model – Logistic Term Birds Humans ci2 – limited growth term

  28. Quadratic Fit p(t) to Data

  29. Exponential Fit i(t)=i0ekt

  30. Modified Models

  31. Our Findings • Birds aren’t 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 wasn’t enough information about the birds, so we didn’t have a lot of data to work with

  32. 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)

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

  34. 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 <http://www.oie.int/downld/AVIAN%20INFLUENZA/A2004_AI.php>. • "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 <http://www.who.int/csr/disease/avian_influenza/country/cases_table_2008_06_19/en/index.html>. • "Global: Cumulative number of human cases of avian influenza A/(H5N1)." EINet. 6Jul 2008 <http://depts.washington.edu/einet/?a=printArticle&print=5054>. • "Index of /worldfacts/countries." AirNinja . H Brothers Inc. 1 Jul 2008 <http://www.airninja.com/worldfacts/countries/>. • "Central Intelligence Agency ." The World Factbook. CIA. 6 Jul 2008 <https://www.cia.gov/library/publications/the-world-factbook/index.html>.

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

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