Yellow Fever in Senegal HannahIsaac

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

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 public- health/bolesti/krp eljni2.htm e7/science/resources.htm 0.html

Cycles of YF Transmission MOSQUITO MONKEY HUMAN, MONKEY MOSQUITO HUMAN MOSQUITO JungleVillageCity

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 :// grenoble.fr/irem/sergesimplificatio n.htm

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

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

System of Equations: Humans ExposedVaccinated ExposedInfective Vaccinated ImmuneExposed

System of Equations: Humans Infective Recovered Dead The Mathemagician /u/math/sjg/simpsonsmath/index.html

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

Parameters Humans: Humans: Population: N H = Population: N H = 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)

Parameters Cont’d Mosquitoes: Mosquitoes: Number of Mosquitoes: N M = Number of Mosquitoes: N M = 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

Model vs. Data for 2002 Outbreak Cumulative Cases Days

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

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

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

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

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

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

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

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