Yellow Yellow Fever in Fever in Senegal Senegal Hannah Hannah Isaac Isaac
Dec 17, 2015
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