The document summarizes several mathematical models of disease transmission dynamics, both with and without interventions. It presents models for transmission intensity and proportion infected under different scenarios. Figures show model outputs like the relationship between transmission intensity and proportion infected, as well as the impact of challenge dose and susceptibility on infection levels. The document cites several references and includes a map showing disease data from communities around the world.

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.

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

7. Brazil
Portugal

10. ILI(t) = p(t)I(t)
€