1. Yellow Fever in Senegal HannahIsaac

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

3. Disease Background First account of sickness diagnosed as YF occurred in 1648 First account of sickness diagnosed as YF occurred in 1648 Causative agent: genus Flavivirus Causative agent: genus Flavivirus Vector: Aedes aegypti (mosquito) Vector: Aedes aegypti (mosquito) Nonhuman primates maintain disease Nonhuman primates maintain disease http://www.tel.hr/ public- health/bolesti/krp eljni2.htm http://www.gemsvt.org/middle/grad e7/science/resources.htm http://www.ahajokes.com/crt05 0.html

4. Cycles of YF Transmission MOSQUITO MONKEY HUMAN, MONKEY MOSQUITO HUMAN MOSQUITO JungleVillageCity www.who.int

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

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

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

8. System of Equations: Humans ExposedVaccinated ExposedInfective Vaccinated ImmuneExposed

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

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

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

12. Parameters Cont’d Mosquitoes: Mosquitoes: Number of Mosquitoes: N M = 100 000 000 Number of Mosquitoes: N M = 100 000 000 Biting rate: μ = 1/10 (bites/day·mosquito) Biting rate: μ = 1/10 (bites/day·mosquito) Birth rate*: α = 0.11 (mosquitoes/day) Birth rate*: α = 0.11 (mosquitoes/day) Death rate: β = 0.25 (mosquitoes/day) Death rate: β = 0.25 (mosquitoes/day) Incubation rate: ε = 1/12 (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. The “Epidemic Curve” New Cases Days Clear peak at ~20 days, no new Infections after 100 days

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

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

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

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

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

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