Sesi 5. Dynamic of Disease Transmission and Reproductive Rate

(1)

Dynamic of disease

transmission

(2)

Epidemic curve

Basic reproduction number

(3)

Measles in Iceland

(4)

Immunity

6. Worm diseases?

The SIR-model with birth and death

SIR - model

b

g

birth and death

(population size: N)

(5)

The SIR-model with birth and death

SIR - model

b

g

equations:

(population size: N)

(fraction susceptible: s)

N = S + I + R

A measure of the potential for transmission

The basic reproductive number

, R

0

, the mean number of individuals directly

infected by

an infectious case

through the total infectious period, when

introduced to a susceptible population

R

₀

=

p

• c

• d

contacts per unit time

probability of transmission per contact

duration of infectiousness

Infection will ….. disappear, if

R < 1

become endemic, if

R = 1

become epidemic, if

R > 1

(www)

(6)

Endemic - Epidemic - Pandemic

v

Endemic

vTransmission occur, but the number of cases remains

constant

v

Epidemic

vThe number of cases increases

v

Pandemic

vWhen epidemics occur at several continents –global

epidemic

(7)

p

condoms, acyclovir, zidovudine

c

health education, negotiating skills

D

case ascertainment (screening, partner notification), treatment,

compliance, health seeking behaviour, accessibility of services

R

0

=

p

• c

• d

(www)

Reproductive Number, R

₀

Use in STI Control

p, transmission probability per exposure– depends on the infection vHIV, p(hand shake)=0, p(transfusion)=1, p(sex)=0.001 vinterventions often aim at reducing p

vuse gloves, screene blood, condoms

c, number of contacts per time unit– relevant contact depends on infection vsame room, within sneezing distance, skin contact,

vinterventions often aim at reducing c

vIsolation, sexual abstinence

d, duration of infectious period

vmay be reduced by medical interventions (TB, but not salmonella)

(www)

(8)

(Anderson & May, 1991)

infection required level

malaria

(P. falciparum, hyperendemic region)

99%

measles 90 – 95%

rubella 82 – 87%

poliomyelitis 82 – 87%

diphteria 82 – 87%

scarlet fever 82 – 87%

smallpox 70 - 80%

SARS 67%

Critical vaccination level for eradication

(9)

Immunity –

herd immunity

vIf R0is the mean number of secondary cases in a susceptible population, then R is the mean number of secondary cases in a population where a proportion, p, are immune

R = R0– (p • R0)

vWhat proportion needs to be immune to prevent epidemics? If R0is 2, then R < 1 if the proportion of immune, p, is > 0.50 If R0is 4, then R < 1 if the proportion of immune, p, is > 0.75

vIf the mean number of secondary cases should be < 1, then R0– (p • R0) < 1

p > (R0– 1)/ R0 = 1 – 1/ R0

vIf R0=15, how large will p need to be to avoid an epidemic?

p > 1-1/15 = 0.94

vThe higher R0, the higher proportion of immunerequired for herd immunity

However ...

1. No heterogeneity ?? ...

2. 100% vaccine efficacy ?? ...

3. Time to establish eradication ...

– childhood diseases

– adulthood diseases

4. Tuberculosis ...

– role of BCG?

– BCG efficacy decreases with age?

(10)

Herd immunity

• a type of

immunity

that occurs when the

vaccination

of a portion of the

population

(or

herd) provides protection to unvaccinated

individuals.

• If a large percent of the population is immune, the

entire population is likely to be protected, not just

those who are immune.

(11)

Why do we have to think about

heterogeneity?

Measles outbreak (almost 3000 cases) despite coverage of 96%

Host heterogeneity

• Disease independent (can be measured also for

non-infected individuals):

• Age, sex, other demographic variables

• Behaviour (e.g. number of contacts, compliance with

vaccination)

• Disease dependent (only for infected individuals):

• Transmission route

• Disease stage; primary versus secondary infection

(12)