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Gabriela Gomes
Instituto Gulbenkian de Ciência, Portugal
Figure 1
A

Colored (intervention) :
dsv (x)
= q(x) µ − xλsv (x),
dt
1
div (x)
= xλsv (x) − µiv (x), λ = β iv (x)dx.
0
dt

1
0.8
0.6
0.4
0.2

∫

0

10

B

Black (no intervention) :
M = 1 − e− pd .
Colored (intervention) :
M =1−

€

1

∫ 0 e−xpd q(x)dx.

2

10
transmission intensity, R

0

1
proportion infected

€

density

λ = βI.

proportion infected

Black (no intervention) :
dS
= µ − λS − µS,
dt
dI
= λS − µI,
dt

0.8
0.6
0.4
0.2
0

5

10
challenge dose, d

10

10

0
0.5
1
susceptibility

Gomes et al 2013 PLOS Pathogens (in review).
data from 90 communities

di(x)
= β [1 − i(x)] − f ( β,r)i(x),
dt
where
β
f ( β,r) = β r
.
e
−1

€

Smith et al 2005 Nature 438: 492.
Gomes et al 2012 Proc R Soc Lond B 279: 2473.
data from 14 communities

Cape
Town
China

Taiwan

Australia
Denmark

Houston
Spain

Lombardy
US & Canada

India
Madras Malawi
Rwanda

Bangladesh
Brazil
Portugal
ILI(t) = p(t)I(t)

€
Gabriela gomes: Mathematical Modeling and Data Needs

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Gabriela gomes: Mathematical Modeling and Data Needs

  • 1. Gabriela Gomes Instituto Gulbenkian de Ciência, Portugal
  • 2. Figure 1 A Colored (intervention) : dsv (x) = q(x) µ − xλsv (x), dt 1 div (x) = xλsv (x) − µiv (x), λ = β iv (x)dx. 0 dt 1 0.8 0.6 0.4 0.2 ∫ 0 10 B Black (no intervention) : M = 1 − e− pd . Colored (intervention) : M =1− € 1 ∫ 0 e−xpd q(x)dx. 2 10 transmission intensity, R 0 1 proportion infected € density λ = βI. proportion infected Black (no intervention) : dS = µ − λS − µS, dt dI = λS − µI, dt 0.8 0.6 0.4 0.2 0 5 10 challenge dose, d 10 10 0 0.5 1 susceptibility Gomes et al 2013 PLOS Pathogens (in review).
  • 3. data from 90 communities di(x) = β [1 − i(x)] − f ( β,r)i(x), dt where β f ( β,r) = β r . e −1 € Smith et al 2005 Nature 438: 492.
  • 4.
  • 5. Gomes et al 2012 Proc R Soc Lond B 279: 2473.
  • 6. data from 14 communities Cape Town China Taiwan Australia Denmark Houston Spain Lombardy US & Canada India Madras Malawi Rwanda Bangladesh
  • 8.
  • 9.