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Yellow Fever in Senegal

Yellow Fever in Senegal. Hannah Isaac. Outline. Disease Background Model Comparison with Data Model Predictions Conclusions and Further Work. Disease Background. First account of sickness diagnosed as YF occurred in 1648 Causative agent: genus Flavivirus

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Yellow Fever in Senegal

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  1. Yellow Fever in Senegal Hannah Isaac

  2. Outline • Disease Background • Model • Comparison with Data • Model Predictions • Conclusions and Further Work

  3. Disease Background • First account of sickness diagnosed as YF occurred in 1648 • Causative agent: genus Flavivirus • Vector: Aedes aegypti (mosquito) • Nonhuman primates maintain disease http://www.tel.hr/public-health/bolesti/krpeljni2.htm http://www.gemsvt.org/middle/grade7/science/resources.htm http://www.ahajokes.com/crt050.html

  4. Cycles of YF Transmission Jungle Village City MOSQUITO MOSQUITO MOSQUITO HUMAN, MONKEY HUMAN HUMAN MONKEY MOSQUITO MOSQUITO MOSQUITO www.who.int

  5. Model Simplifications • Endemic presence of disease in the jungle • Consider urban outbreak only • Disease brought to city though movement of infected humans (initial condition) http://www.ac-grenoble.fr/irem/sergesimplification.htm

  6. Exposed* Infective** Recovered*** Susceptible Vaccinated *Virus incubating **Contagious ***Includes: survivors, victims, Immune The SEVIR Model Humans can be in one of five categories at a time

  7. Assumptions • 100% transmission • Linear vaccination term, 1 week lag • Pesticides affect the birth rate continuously • No mosquito larval stage • Homogeneous mixing of people

  8. Exposed Vaccinated Vaccinated Immune Exposed Exposed Infective System of Equations: Humans

  9. Infective Recovered Dead System of Equations: Humans The Mathemagician http://www.mathsci.appstate.edu/u/math/sjg/simpsonsmath/index.html

  10. Birth Death & Infective Exposed Exposed Birth & Death Death Infective System of Equations: Mosquitoes

  11. Parameters • Humans: • Population: NH = 800 000 • Incubation rate: δ = 1/12 (people/day) • Death rate: ψ = 0.08/14 (people/day) • Recovery rate: r = 0.92/14 (people/day) http://www.aclassmedicine.org/diet.html

  12. Parameters Cont’d • Mosquitoes: • Number of Mosquitoes: NM = 100 000 000 • Biting rate: μ = 1/10 (bites/day·mosquito) • Birth rate*: α = 0.11 (mosquitoes/day) • Death rate: β = 0.25 (mosquitoes/day) • Incubation rate: ε = 1/12 (mosquitoes/day) *Low due to insecticide use

  13. Model vs. Data for 2002 Outbreak Cumulative Cases Days

  14. New Cases Days The “Epidemic Curve” Clear peak at ~20 days, no new Infections after 100 days

  15. Predictive Power • Parameters can be changed to make useful predictions: • Changing control parameters • Varying disease introduction

  16. Cumulative Cases Days Without Pesticide Controlled epidemic (vaccine) with a higher number of total cases (~400)

  17. Cumulative Cases Days Without Vaccine Controlled epidemic (pesticide) with a higher number of total cases (~450)

  18. Cumulative Cases Days No Controls (pesticide or vaccine) Disease is rampant!

  19. Cumulative Cases Days Introduction of Disease Through Pre-Contagious Humans Vaccine takes effect before contagious period begins

  20. Conclusions • Single urban compartment well-described by model • Parameter adjustment has realistic effects • Future models should include progression through jungle and village

  21. Thanks to... Gary, Joanna, Alex, and all the other instructors and math campers Math Camp

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