1 Department of Infectious Disease Epidemiology, Faculty of Medicine, Imperial College London The impact of vaccination on the epidemiology of infectious

1Department of Infectious Disease Epidemiology, Faculty of Medicine, Imperial College London

The impact of vaccination on the epidemiology of infectious diseases

(lecture 1)Roy Anderson

Department of Infectious Disease EpidemiologyFaculty of Medicine,

Imperial College London

New Delhi, India - September 19th 2011


Contents-Lecture 1

• History.• Basic epidemiological principles.• Criteria for eradication.• Heterogeneities.• Impact of mass vaccination on

epidemiological pattern.• Conclusions.

Epidemiccurves


Vaccines as a fraction of total pharmaceutical sales in total – worldwide in 2006

Total sales - $ 380 billion


Geographical distribution of vaccine market share April 2011


Vaccine Trails - Stages

• Pre-clinical 2 years• Phase 1 10-1000• Phase 2 100-1000• Phase 3 10,000-70,000• Phase 4 100,000-1,000,000

Stage Number of people in trial

Time from proof of concept to market – of the order of 10 years or longer


Measles – England & Wales


Pertussis notifications – England & Wales


Emergence of P3 strains of Bordetella pertussis


Sero-surveillance – mumps - Netherlands


Hib (Haemophilus influenzae type b) Vaccination – England & Wales


Pneumococcal disease age distribution - Netherlands


Basic epidemiological principles


Stochasticity & persistence

Disease extinction likely by chance when number of infectives falls to very low numbers.

- so extinction more frequent as population size decreases and cycle amplitudes increase.


Critical community sizeMinimum population size at which measles fadeouts (proportion of weeks with no cases) become rare.

TRUE


Seasonality in transmission of measles – school holidays

0

20

40

60

1 11 21 31 41 51

RCGP Model

Week

Inc

ide

nc

e

Confidencebar


HIV-1 prevalence in Nairobi, Kenya 1981-1999 – stratified by risk group

Year

% in

fected w

ith H

IV-

1

Sex workersMen with GUDPregnant women

Sex workersMen with GUDPregnant women

Pregnant womenPregnant women

Men with GUDMen with GUD

Sex workersSex workers


Daniel Bernoulli - 1700 to 1782

D. Bernoulli (1760)used a simple mathematical

model to evaluate the effectiveness of variolation to

protect against smallpox.

Daniel Bernoulli was one of a number of early mathematicians

who turned their skills to probability problems raised by gamblers - perhaps at the card

tables in Monte Carlo (e.g. C. Huyghens 1657).


Basic principles in Infectious Disease Epidemiology

• The key determinant of incidence and prevalence of infection is the basic reproductive number Ro.

• Ro measures the average number of secondary cases generated by one primary case in a susceptible population

• Many factors determine its magnitude, including those that influence the typical course of infection in the patient and those that determine transmission between people.


Basic Reproductive number, Ro

Chains of transmission between hosts

Generation 1 2 3 4 5 6 7 8

Number Infected

R11 2 2 3 4 6 7

1 1.5 1.33 1.5 1.16

R0 Basic reproduction numberaverage no. of secondary cases generated by 1 primary case in a susceptible population

Rt Effective reproduction number number of infections caused by each new case occurring at time, t

• The key determinant of incidence and prevalence of infection is the basic reproductive number Ro.

• Many factors determine its magnitude, including those that influence the typical course of infection in the patient and those that determine transmission between people.


The epidemic curveR

ate

of

new

in

fect

ion

s

establishment exponentialgrowth

Time

exhau

stion

of

suscep

tibles

endemicity

Equilibrium, or recurrent epidemics

y e

(R0 -1

)/TG t

Random (stochastic)effects


Typical course of infection within the host

Estimation of average latent & infectious periods plus distributions


Viral load over course of infection as a function of patient age (influenza A - viral titre AUC versus age)

100

200

300

400

500

600

700

800

900

Vir

al t

itre

AU

C(l

og

10 T

CID

50

h/m

L)

0 10 20 30 40 50 60 70 800

Age (years)90 100

Line of regression

95% confidence limits for mean predicted value

Osterhaus, Oxford, Jackson, & Ward (2001)


The typical course of infection

0

10

20

30

40

50

60

70

80

90

100

Days post onset of clinical symptoms

Per

cen

tag

e o

f sa

mp

les

po

siti

ve

Naso pharangeal aspirate Stool Urine

1

10

100

1000

10000

1 2 3 4 5 6 7 8 9

days post viral inoculation

viral t

iter (l

og 10

)0

5

10

15

sympto

m sco

re

Viral load

Symptom score

Influenza ASARS CoV

* Hayden et al. (1998) J. Clin Invest 101 p643Experimental human influenza A/Texas/36/91 (H1N1) intranasal inoculation 105 dose Peiris et al (2003)



• The magnitude of Ro varies according to location and population - it is strongly influenced by birth rate, population density and behavioural factors.

• The magnitude of Ro can be ascertained by cross sectional serological surveys.


What is Herd Immunity?

• The impact of the fraction immune in the community on the per capita rate of transmission of an infectious agent.

• The level of herd immunity can be measured by reference to the magnitude of reduction in the value of Ro.


How can the degree of herd immunity and the magnitude of Ro be assessed?

• Cross-sectional and longitudinal serological surveys.

• Serum and saliva (viral infections).• Activated T cells (bacteria and protozoa)?• Quantitative assays.


Scientific methods in the study of herd immunity

• Immunological and Disease Surveillance methods provide the empirical base for analysis and interpretation.

• Mathematical & statistical methods play an important role in the analysis of infectious disease transmission and control.

• They help to define both what needs to be measured, and how best to measure define epidemiological quantities.


Age in Years

Prop

ortion S

eropositive

0 2.5 5 7.5 10 12.5 15 17.5 20

1

0.9

0.8

0.7

0.6

0.5

0.4

0.3

0.2

0.1

0

Maternal Antibodies Antibodies from Infection

Age-specific serology

Used to calculate the average age at infection, A, the average

duration of maternal antibody protection, M, and the degree

of herd immunity

Used to calculate the average age at infection, A, the average

duration of maternal antibody protection, M, and the degree

of herd immunity


Serological profile - Varicella virus

(Schneweis et al, 1985 - Germany)


Force or rate of infection λ and the average age of infection A – estimation from serology (1)

If the proportion seropositive at age a is p(a), then the average force or rate of infection λ over the interval 0 to a years of age is given by:

λ(a)=p(a)/[L(1-e(-a/L))]; eq(1)

where L is life expectancy. Other relationships of importance are:

A≈1/λ; eq(2)

R0≈L/A; eq(3)and pc=(1-1/R0)=(1-A/L). eq(4)

Here R0 is the basic reproductive number (average number of secondary cases generated by one primary case, and pc is the critical fraction to be vaccinated to block transmission.



A simple worked example is as follows. Consider measles where 70% of children are seropositive at age 3 years (p(3)=0.7), and life expectancy is 60 years. Using the equations in the previous slide:

from eqn(1) λ = 0.2392 yr-1;

the average age at infection, A = 4.18 years;

R0 = 14.35; and

pc = 0.93, or 93% coverage.

In reality many complications slightly alter these values. One important example is maternal antibodies which have a half life of 6 months in well nourished mothers who breast feed. This value (0.5 yrs) should be subtracted from a in the calculation of λ – which gives a required coverage of 94.2% (see Anderson & May (1991) for fuller discussion)


The calculation of the magnitude of Ro

A series of simple relationships exist between keyepidemiological, demographic and vaccination programme related parameters.

The magnitude of Ro and the average at infection prior to mass vaccination, A, plus life expectancy in the population are related as follows

)/()( MAALRo )/()( MAALRo Here, M is the average duration of maternal antibody protection (6 months) and L is life expectancy



Some examples of studies from which the data employed in the previous calculations can be derived. Serology for Rubella virus in the UK (see

Anderson & May (1991))

Decay in maternal antibodies Longitudinal and cross-sectional serological surveys


Mumps Virus - Age-specific change in the per capita rate of infection (Anderson & May 1983)

0.5-2 3-5 6-8 9-14 15+0

0.5

1

1.5

2

2.5

Age in years

Fo

rce o

f infe

ction

/ann

um


Human Parvovirus B19 serology – force of

infection (FOI) by ageMossong et al (2008) Parvovirus B19 infection in five European countries: seroepidemiology, force of infection and maternal risk of infection. Epidemiol. Infect. (2008), 136, 1059–1068

Belgium

England

Finland

Poland

Italy Age (years)

Forc

e of

Infe

ction

(FO

I)

% S

erop

ositi

ve


Parameters – Who mixes with Whom• Wallinga J, Teunis P, Kretzschmar M. (2006) Using data on social contacts

to estimate age-specific transmission parameters for respiratory-spread infectious agents. American Journal of Epidemiology 164, 936–944.

• Beutels P, et al. (2006) Social mixing patterns for transmission models of close contact infections : exploring self-evaluation and diary-based data collection through a web-based interface. Epidemiology and Infection. 134, 1158–1166.

• Edmunds WJ, O’Callaghan CJ, Nokes DJ. (1997) Who mixes with whom? A method to determine the contact patterns of adults that may lead to the spread of airborne infections. Proceedings of the Royal Society of London, Series B: Biological Sciences 264, 949–957.

• Farrington CP. (1990) Modelling forces of infection for measles, mumps and rubella. Statistics in Medicine 9, 953–967.


Average age, A, at infection prior to immunisation

Infection Average age at infection, A

Location/time period

Measles virus 5-6 years

2-3 years

USA 1955-58

Bangkok, Thailand 1967

Rubella virus 9-10 years Sweden 1965

Varicella virus 6-8 years USA 1921-28

Polio virus 12-17 years USA 1920-60

Mumps virus 7-8 years England & Wales 1975

Smallpox virus 10-15years Bangladesh 1940


Estimates of the basic reproductive number, Ro

Infection Location Time period Ro

Measles England

Canada

1947-50

1912-13

13-15

11-13

Varicella USA 1943 7-8

Mumps Netherlands 1970-80 11-14

Rubella West Germany 1970-79 6-7

Polio USA 1955 5-6

HIV-1 Nairobi, Kenya

(sex workers)

1981-85 11-12

Smallpox Bangladesh 1940 4-6

Influenza A (H1N1)

England 2010 1-1.5


Estimation of R0 from past influenza A epidemics


SARS - distribution of R

0

5

10

15

20

25

30

Number

0 2 4 6 8 10 12

Number of secondary cases

Super spreadingevents (person,place & setting)

Rapid SARS Virus Spread in Flats 7 and 8, Block E

Amoy Garden, Hong Kong. 1st March 2003 –

292 people infected by one index case


The generation of secondary cases with vaccination

Generation 1 2 3 4 5 6 7 8

Number Infected

R11 2 2 3 4 5 11 2 1 1.5 1.33 1.25 0.2

Vaccinatedindividuals



The magnitude of pc , the fraction of each birth cohort that must be immunised to block transmission is given bythe following simple expression:,

/]/[][ bLALpc /]/[][ bLALpc

The parameter b is the average age at first vaccination,L is life expectancy (related to the net birth rate), and A is the average age at infection prior to mass immunisation. Vaccine efficacy = ε, ranging from 0-1.


Vaccine efficacy

MEASLES 90%-95%

MUMPS 72%-88%

RUBELLA 95%-98%

(Christensen & Bottiger,1991; Clarkson & Fine,1987; Ramsey et. al.,1994)


Mass vaccinationAnderson, et al (1998) Lancet 350:1466-1470

0.95

0.96

0.97

0.98

0.99

1

Average age at Vaccination V (years)

Fra

ctio

n f

va

ccin

ate

d

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

Fraction that must be vaccinated toblock transmission (A=5 years)

Vaccine efficacy changes with age due to presence of maternal antibodies

Maximumvaccine

efficacy Q

Q=1.0

Q=0.98

Q=0.97


Age at vaccination - good and bad patterns

0

20

40

60

80

% I

mm

un

ized

0- 1- 2- 3- 4- 5- 6- 7- 8- 9- 10-

Age group in years

Good pattern - clusteredaround the optimal age

Poor pattern - spreadto the right side ofthe optimal age


1) Increase in average age at infection

2) Increase in the inter-epidemic period

3) Toughs in susceptibility in the herd immunity profile

4) Changes in the age distribution of infection and serious disease

5) Non-linear relationship between the incidence of infection and disease and vaccine uptake

Predictions based on mathematical models of transmission and the

impact of mass vaccination


Average age of infection - the impact of vaccination

0

10

20

30

40

50

60

0 0.2 0.4 0.6 0.8

Proportion of cohort immunised at age 2 years

Av

era

ge

ag

e a

t in

fec

tio

n (

yrs

)

Average age of infectionprior to vaccination set at 5 years.

Average age of vaccination setat 2 years.


Vaccination - and the age distribution of infection


Impact of vaccination on serology


Herd immunity profile - across age classes and through time

(Anderson and May, 1982; Science 215:1053-60).

Measles - serology post the introduction of a cohort based vaccination programme


<1m

1-m

6-m

1-

2-

4-

6-

8-

10-

12-

14-

16-

20-

25-

30-

40-

>600

0.2

0.4

0.6

0.8

1

19791981

19831985

19871989

1991

Age

Fra

ction

sero

po

sitive

<1m

1-m

6-m

1-

2-

4-

6-

8-

10-

12-

14-

16-

20-

25-

30-

40-

>600

0.2

0.4

0.6

0.8

1

19791981

19831985

19871989

1991

Age

Fra

ction

sero

po

sitive

Female Male

Age stratified & longitudinal serologyfor Rubella antibodies. Finland 1979-91

(Ukkonen et al, 1995)


0

0.5

1

1.5

2

2.5

0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Proportion Vaccinated

Ra

tio

of

ca

se

s a

fte

r/b

efo

reMass vaccination can increase the incidence

of serious disease if the likelihood rises with age per case of infection

(Anderson & May, 1983; J. Hygiene 90:259-325)

The case of rubella and congenital rubella syndrome


Percentage gain from the indirect effects of herd immunity

0

20

40

60

80

100

0.75 0.85 0.95

Proportion of cohort vaccinated

% g

ain

fro

m i

nd

ire

ct e

ffe

cts

Critical vaccinationcoverage to block

transmission, pc


Ferguson et al, 2006 – Nature - on line

April 27th 2006

Individual based stochastic simulation model with three scales of mixing – extensive

sensitivity analysis and analysisof past influenza epidemics

200 days compressedinto a few seconds


Conclusions• Eradication difficult when Ro large and population density plus net

birth rate high.• Heterogeneity in population density and vaccine coverage important.• Carrier state important as are reservoir hosts (if involved).• Mathematical & computational methods permit analytical &

simulation studies of potential impact of different strategies.• Cost benefit studies need to take account of indirect effects of mass

vaccination on transmission.• Vaccine coverage must be maintained at high levels to avoid the

immigration of infectives stimulating epidemics in susceptible pockets.• Imperfect vaccines – phase IV monitoring of vital importance.• Multi- strain systems – more research required – will new strains

replace those targeted by a multi-valent vaccine?


The End


Mass vaccination programmes for infections where the incidence of serious disease rises with age at

infection (e.g. Rubella)Rubella. The equilibrium ration of rubella cases in pregnant women in the age range 16-40 years after vaccination of a proportion p)the horizontal axis). At age V years divided by cases before vaccination. The fertility function used to derive this graph is displayed below. The vaccination policy adopted is for vaccination of boys and girls around one year of age (V=1).

A is the average age of infection in years for

rubella prior to immunisation.


Rubella vaccination programmes in the UK – change in policy (Anderson & May, 1983)

The ratio of cases of infection in 16-40 year old women after vaccination divided by before for tow different policies – vaccinated boys and girls at 2 years of age, and vaccinating girls only at 12 years of age. The dark shaded regions denote where a policy could make matters worse. In the UK with coverage above 80% no problem arises


Spatial de-correlation inducedby vaccination - measles

Viewing de-correlation

Epidemics initially highly synchronised before vaccination, then increasingly de-correlated post-vaccination.

Spatial

location

Den

sity of cases


• High performance, object-oriented code. Intended to be scaleable to allow 000s of model simulations of 60 million population to be performed.

• Computationally intensive (>5GB memory use for 60 million).

• Three levels of population structure:

• Flexible modelling of disease biology (arbitrary distributions, number of disease stages), and interventions (ring vaccination, mass vaccination, quarantine, anti-viral treatment, movement constraints).

Model design for individual based stochastic simulations

Household Network(disease specific)

Distance

Pro

ba

bili

ty

Spatial


Spatial kernels – mobile phone data – frequency versus – distanced moved per defined time unit

1

10

100

1000

10000

100000

1000 10000 100000 1000000

Sum over daily legs

Legs

Daily Extent

Distance metres

Nu

mb

er of

peo

ple


Data needs: detailed population data: Landscan (Oakridge Natl. Lab.)

Need both population data (density, age, household)and mixing/travel data.

Population density – based on satellite imagery


HIV-1 vaccines• At present, there are many ongoing HIV-1 vaccine trials and

several pending for 2006, involving different vaccines (of which some are DNA-based, some use recombinant viral vectors, 4 are protein subunits and 3 are lipopeptide-based).

• Most are in Phase I, with VaxGen’s two trials (in North America and Thailand) the only Phase III studies completed. Both Phase III trials were completed in 2003, with efficacy data revealing no difference in infection in treated and untreated arms.

• The majority use clade B strains, but a few candidates (especially among the newer ones in the pipeline) are based on clades A, C, D and E (http://www.iavi.org).


Eradication criterion – protective vaccines

]/1][/11[ 0 VLR

pc

pc is the critical fraction of each cohort immunised, R0 is the basic reproductive number, L is life expectancy, V is the duration of vaccine protection and ε is

vaccine efficacy


Imperfect vaccines• Vaccinated individuals acquire infection but

show slower progression to AIDS.• Slower progression is linked to lower viral

loads – especially in the primary HIV-1 infection phase.

• Lower viral load is linked to lowered infectiousness to susceptible sexual partners.

• Vaccination may be linked to increased risk behaviours.


]/1[

]/1][/11[

00

0

RR

VLRp

vc

Eradication criterion – imperfect vaccines

pc is the critical fraction of each cohort immunised, R0 is the basic reproductive

number for unvaccinateds, R0v is the reproductive numbers for vaccinateds,

L is life expectancy, V is the duration of vaccine protection and ε is

vaccine efficacy


Illustrative schematic diagram, in two dimensions, of a multidimensional parameter space denoting the six possible equilibrium states that can exist for different

epidemiological and vaccine property related parameter combinations (Anderson & Hanson, 2005, JID).

No vaccination & endemic persistence of HIV-1 infection

(Ro>1, p=0)

No vaccination & endemic persistence of HIV-1 infection

(Ro>1, p=0)

No persistence of HIV-1 infection

(Ro<1)

No persistence of HIV-1 infection

(Ro<1)

Vaccination & eradication of HIV-1 infection

(yv*=0)

Vaccination & eradication of HIV-1 infection

(yv*=0)

Vaccination & perverse outcome of increased HIV-1 infection& decreased population size

(yv*>y*, Nv*<N*)

Vaccination & perverse outcome of increased HIV-1 infection& decreased population size

(yv*>y*, Nv*<N*)

Vaccination & good outcome

of increased HIV-1 infection

but increased population size

(yv*>y*, Nv*>N*)

Vaccination & good outcome

of increased HIV-1 infection

but increased population size

(yv*>y*, Nv*>N*) Vaccination & good outcome of decreased HIV-1 infection& increased population size

(yv*<y*, Nv*>N*)

Vaccination & good outcome of decreased HIV-1 infection& increased population size

(yv*<y*, Nv*>N*)

Documents

1 Department of Infectious Disease Epidemiology, Faculty of Medicine, Imperial College London The impact of vaccination on the epidemiology of infectious