Yellow Fever in Senegal:Strategies for Control

http://www.fnai.org/ARROW/almanac/history/history_regional_timeline.cfm

Nicholas Eriksson, Heather Lynch, Brendan O’Fallon, Katharine Preedy

Advisor: Simon Levin

World Health Organization: Communicable Diseases Epidemiological Report (2003)

Three patch model:Urban, Village, and Forest

U

V

F~ 1,000 individuals with constant rate of infection from forest (monkey) reservoir

~ 10,000 individuals with infection coming from contact with infected individuals from the forest patch

~ 100,000 individuals with infection coming from contact with infected individuals from the village patch

Urban

Village

Forest

infection from the reservoir

Num

ber

of In

fect

ed In

divi

dual

s

Num

ber

of

Infe

cted

Ind

ivid

ual

s

Time (days)

Time (days)

~ 2.3 years

rate of infection from reservoir = 0.0001/daytransmission-rate = 0.12/infected individual/dayrecovery rate = 0.10/daycontact probability between forest-village = 0.01/infected individual/daycontact probability between village-urban = 0.01/infected individual/daybirth rate = death rate = 0.0001/day

Vaccination =

vaccination rate = 2.5e-4 vaccinations/person/day

Fra

ctio

n of

Day

s S

ampl

ed

Number of Infected Individuals

+

Quarantine 50%

Quarantine 75%

Mea

n U

rban

Infe

cted

Indi

vidu

als

Vaccination Rate

A Comparison of Vaccination Strategies

Further Work:

• pulsed vaccinations• seasonal fluctuations• mosquito population• mosquito-based control

- spraying

- mosquito nets• less parameter-sensitive models

Summary:

• in this model, the most effective vaccination strategy is in the urban patch

• quarantine can be as effective as vaccination if infected individuals can be properly identified

• vaccination is most effective at the ‘tails’ of the infected distribution, i.e. it eliminates the worst outbreaks

Eigenvalues of Equilibrium Point of Homogeneous System

Real part of eigenvalues Imaginary part of eigenvalues

Dominant Eigenvalue

Vaccination vs. Immigration