Yellow Yellow Fever in Fever in SenegalSenegal

Hannah Hannah IsaacIsaac

OutlineOutline

Disease BackgroundDisease Background ModelModel Comparison with DataComparison with Data Model PredictionsModel Predictions Conclusions and Further WorkConclusions and Further Work

Disease BackgroundDisease Background

First account of First account of sickness diagnosed sickness diagnosed as YF occurred in as YF occurred in 16481648

Causative agent: Causative agent: genus Flavivirusgenus Flavivirus

Vector: Aedes Vector: Aedes aegypti (mosquito)aegypti (mosquito)

Nonhuman primates Nonhuman primates maintain diseasemaintain 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

Cycles of YF Cycles of YF TransmissionTransmission

MOSQUITO

MONKEY

HUMAN,

MONKEY

MOSQUITO

HUMAN HUMAN

MOSQUITO

MOSQUITO

MOSQUITO

MOSQUITO

Jungle Village City

www.who.int

Model SimplificationsModel Simplifications

Endemic presence of disease Endemic presence of disease in the junglein the jungle

Consider urban outbreak onlyConsider urban outbreak only

Disease brought to city Disease brought to city though movement of infected though movement of infected humans (initial condition)humans (initial condition)

http://www.ac-grenoble.fr/irem/sergesimplification.htm

The SEVIR ModelThe SEVIR Model

Humans can be in one of five categories at a time

*Virus incubating*Virus incubating**Contagious**Contagious***Includes: survivors, victims, Immune***Includes: survivors, victims, Immune

Susceptible Exposed* Infective** Recovered***

Vaccinated

AssumptionsAssumptions

100% transmission100% transmission

Linear vaccination term, 1 week lagLinear vaccination term, 1 week lag

Pesticides affect the birth rate Pesticides affect the birth rate continuouslycontinuously

No mosquito larval stageNo mosquito larval stage

Homogeneous mixing of peopleHomogeneous mixing of people

System of Equations: System of Equations: HumansHumans

d

d

t( )SH t

( )TM t ( )SH t

NHv ( )SH t

Exposed Vaccinated

d

d

t( )EH t

( )TM t ( )( )SH t ( )VH t

NH

( )EH t

Exposed Infective

d

d

t( )VH t

v ( )SH t ve ( )VH t

( )TM t ( )VH t

NH

Vaccinated Immune Exposed

System of Equations: System of Equations: HumansHumans

d

d

t( )TH t

( )EH t

d

d

t( )RH t r ( )TH t

d

d

t( )DDH t

( )TH t

Infective

Recovered

Dead

The Mathemagician

http://www.mathsci.appstate.edu/u/math/sjg/simpsonsmath/index.html

System of Equations: System of Equations: MosquitoesMosquitoes

d

d

t( )EM t ( ) ( )EM t

( )TH t ( )SM t

NH

( )( )EM t ( )TM t

Death & Infective Exposed Birth

d

d

t( )SM t

( )TH t ( )SM t

NH( ) ( )SM t

Exposed Birth & Death

d

d

t( )TM t ( )TM t ( )EM t

Death Infective

ParametersParameters

Humans:Humans: Population: NPopulation: NH H = 800 000= 800 000

Incubation rate: Incubation rate: δδ = 1/12 = 1/12 (people/day)(people/day)

Death rate: Death rate: ψψ = 0.08/14 = 0.08/14 (people/day)(people/day)

Recovery rate: r = Recovery rate: r = 0.92/14 (people/day)0.92/14 (people/day) http://

www.aclassmedicine.org/diet.html

Parameters Cont’dParameters Cont’d

Mosquitoes:Mosquitoes:

Number of Mosquitoes: NNumber of Mosquitoes: NMM = 100 000 000 = 100 000 000

Biting rate: Biting rate: μμ = 1/10 (bites/day·mosquito) = 1/10 (bites/day·mosquito)

Birth rate*: Birth rate*: αα = 0.11 (mosquitoes/day) = 0.11 (mosquitoes/day)

Death rate: Death rate: ββ = 0.25 (mosquitoes/day) = 0.25 (mosquitoes/day)

Incubation rate: Incubation rate: εε = 1/12 (mosquitoes/day) = 1/12 (mosquitoes/day)

*Low due to insecticide use*Low due to insecticide use

Model vs. Data for 2002 Model vs. Data for 2002 OutbreakOutbreak

Cu

mu

lati

ve

Cases

Days

The “Epidemic Curve”The “Epidemic Curve”N

ew

Cases

Days

Clear peak at ~20 days, no newInfections after 100 days

Predictive PowerPredictive Power

Parameters can be changed to Parameters can be changed to make useful predictions:make useful predictions:

Changing control parametersChanging control parameters Varying disease introductionVarying disease introduction

Without PesticideWithout PesticideC

um

ula

tive

Cases

Days

Controlled epidemic (vaccine) with a higher number of total cases (~400)

Without VaccineWithout VaccineC

um

ula

tive

Cases

Days

Controlled epidemic (pesticide) with a higher number of total cases (~450)

No Controls (pesticide or No Controls (pesticide or vaccine)vaccine)

Cu

mu

lati

ve

Cases

Days

Disease is rampant!

Introduction of Disease Introduction of Disease Through Through Pre-Contagious HumansPre-Contagious Humans

Cu

mu

lati

ve

Cases

Days

Vaccine takes effect before contagious period begins

Conclusions Conclusions

Single urban compartment well-Single urban compartment well-described by modeldescribed by model

Parameter adjustment has realistic Parameter adjustment has realistic effectseffects

Future models should include Future models should include progression through jungle and progression through jungle and villagevillage

Thanks to...Thanks to...

Gary, Joanna, Alex, and all the other instructors and math campers

Math Camp