1. Department of Infectious Disease Epidemiology Imperial College London
The impact of vaccination on the epidemiology of infectious diseases (lecture 1)
Roy Anderson
Department of Infectious Disease Epidemiology
Faculty of Medicine,
Imperial College London
New Delhi, India - September 19th 2011

2. Contents-Lecture 1 History. Basic epidemiological principles.
Criteria for eradication.
Heterogeneities.
Impact of mass vaccination on epidemiological pattern.
Conclusions.
Epidemic
curves

3. Vaccines as a fraction of total
pharmaceutical sales in total – worldwide in 2006
Total sales - $ 380 billion

4. Geographical distribution of vaccine market share April 2011

5. Vaccine Trails - Stages
Stage Number of people in trial
Pre-clinical years
Phase
Phase
Phase ,000-70,000
Phase ,000-1,000,000
Time from proof of concept to market – of the order of 10 years or longer

6. Measles – England & Wales

7. Pertussis notifications – England & Wales

8. Emergence of P3 strains of Bordetella pertussis

9. Sero-surveillance – mumps - Netherlands

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

11. Pneumococcal disease age distribution - Netherlands

12. Basic epidemiological principles

13. 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.

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

15. Seasonality in transmission of measles – school holidays
Confidence
bar

16. HIV-1 prevalence in Nairobi, Kenya 1981-1999 – stratified by risk group
% infected with HIV-1
Sex workers
Men with GUD
Pregnant women
Sex workers
Men with GUD
Pregnant women
Year

17. Daniel Bernoulli was one of a number of early mathematicians
Daniel Bernoulli 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).

18. 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.

19. Basic Reproductive number, Ro
Chains of transmission between hosts
Generation 1 2 3 4 5 6 7 8
Number Infected R
1.5
1.33
1.16
R0 Basic reproduction number
average 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.

20. exhaustion of susceptibles Equilibrium, or recurrent epidemics
The epidemic curve
Rate of new infections
establishment
exponential
growth
Time
exhaustion of susceptibles
endemicity
Equilibrium, or recurrent epidemics
y  e(R0-1)/TG t
Random (stochastic)
effects

21. Typical course of infection within the host
Estimation of average latent & infectious periods plus distributions

22. Viral load over course of infection as a function of patient age (influenza A - viral titre AUC versus age)
900
Line of regression
Osterhaus, Oxford, Jackson, & Ward (2001)
95% confidence limits for mean predicted value
800
700
600
Viral titre AUC (log10 TCID50h/mL)
500
400
300
200
100 10 20 30 40 50 60 70 80
Age (years) 90
100

23. The typical course of infection
SARS CoV
Influenza A
Viral load
Symptom
score
* Hayden et al. (1998) J. Clin Invest 101 p643
Experimental human influenza A/Texas/36/91 (H1N1)
intranasal inoculation 105 dose
Peiris et al (2003)

24. Basic principles in Infectious Disease Epidemiology
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.

25. 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.

26. 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.

27. 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.

28. Age-specific serology
Age in Years
Proportion Seropositive
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
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

29. Serological profile - Varicella virus (Schneweis et al, 1985 - Germany)

30. 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.

31. Force or rate of infection λ and the average age of infection A – estimation from serology (2)
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 = 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)

32. The calculation of the magnitude of Ro
A series of simple relationships exist between key
epidemiological, 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
Here, M is the average duration of maternal antibody
protection (6 months) and L is life expectancy

33. Force or rate of infection λ and the average age of infection A – estimation from serology (3)
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

34. Mumps Virus - Age-specific change in the
per capita rate of infection (Anderson & May 1983)
2.5 2
1.5
Force of infection/annum 1
0.5
0.5-2
3-5
6-8
9-14
15+
Age in years

35. Human Parvovirus B19 serology – force of infection (FOI) by age Mossong 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
% Seropositive
Force of Infection (FOI)
Italy
Age (years)

36. 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.

37. Average age, A, at infection prior to immunisation
Average age at infection, A
Location/time period
Measles virus
5-6 years
2-3 years
USA
Bangkok, Thailand 1967
Rubella virus
9-10 years
Sweden 1965
Varicella virus
6-8 years
USA
Polio virus
12-17 years
USA
Mumps virus
7-8 years
England & Wales 1975
Smallpox virus
10-15years
Bangladesh 1940

38. Estimates of the basic reproductive number, Ro
Infection
Location
Time period Ro
Measles
England
Canada
13-15
11-13
Varicella
USA
1943
7-8
Mumps
Netherlands
11-14
Rubella
West Germany
6-7
Polio
1955
5-6
HIV-1
Nairobi, Kenya
(sex workers)
11-12
Smallpox
Bangladesh
1940
4-6
Influenza A (H1N1)
2010
1-1.5

39. Estimation of R0 from past influenza A epidemics

40. SARS - distribution of R
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
Super spreading
events (person,
place & setting)

41. The generation of secondary cases with vaccination1 2 3 4 5 6 7 8
Number Infected R
1.5
1.33
1.25
0.2
Vaccinated
individuals

42. Basic principles in Infectious Disease Epidemiology
The magnitude of pc , the fraction of each birth cohort
that must be immunised to block transmission is given by
the following simple expression:,
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.

43. Vaccine efficacy MEASLES 90%-95% MUMPS 72%-88% RUBELLA 95%-98%
(Christensen & Bottiger,1991; Clarkson & Fine,1987; Ramsey et. al.,1994)
MEASLES
90%-95%
MUMPS
72%-88%
RUBELLA
95%-98%

44. Mass vaccination Anderson, et al (1998) Lancet 350:1466-1470
0.95
0.96
0.97
0.98
0.99 1
Fraction that must be vaccinated to
block transmission (A=5 years)
Q=0.97
Q=0.98
Fraction f vaccinated
Maximum
vaccine
efficacy Q
Q=1.0
0.5 1
1.5 2
2.5 3
3.5 4
4.5 5
Average age at Vaccination V (years)
Vaccine efficacy changes with age due to
presence of maternal antibodies

45. Age at vaccination - good and bad patterns
Poor pattern - spread
to the right side of
the optimal age
Good pattern - clustered
around the optimal age

46. Predictions based on mathematical models of transmission and the
impact of mass vaccination
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

47. Average age of infection - the impact of vaccination
prior to vaccination
set at 5 years.
Average age of
vaccination set
at 2 years.

48. Vaccination - and the age distribution of infection

49. Impact of vaccination on serology

50. Herd immunity profile - across age classes and through time (Anderson and May, 1982; Science 215: ).
Measles - serology post the introduction of a cohort
based vaccination programme

51. Age stratified & longitudinal serology for Rubella antibodies
Age stratified & longitudinal serology for Rubella antibodies. Finland
<1m
1-m
6-m 1- 2- 4- 6- 8-
10-
12-
14-
16-
20-
25-
30-
40-
>60
0.2
0.4
0.6
0.8 1
1979
1981
1983
1985
1987
1989
1991
(Ukkonen et al, 1995) 1
0.8
Fraction seropositive
0.6
Fraction seropositive
0.4
1991
Female
Male
1989
0.2
1987
1985
1983
1981
1979
<1m
6-m 2- 6-
10-
14-
20-
30-
>60
1-m 1- 4- 8-
12-
16-
25-
40-
Age
Age

52. Mass vaccination can increase the incidence
of serious disease if the likelihood rises
with age per case of infection
(Anderson & May, 1983; J. Hygiene 90: )
The case of rubella and congenital
rubella syndrome

53. Percentage gain from the indirect effects of herd immunity
Critical
vaccination
coverage
to block
transmission, pc

54. Ferguson et al, 2006 – Nature - on line April 27th 2006
200 days compressed
into a few seconds
Ferguson et al, 2006 – Nature - on line April 27th 2006
Individual based stochastic
simulation model with three
scales of mixing – extensive
sensitivity analysis and analysis
of past influenza epidemics

55. 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?

56. The End

57. rubella prior to immunisation.
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.

58. 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

59. Spatial de-correlation induced by vaccination - measles
Viewing de-correlation
Density of cases
Spatial location
Epidemics initially highly synchronised before vaccination, then increasingly de-correlated post-vaccination.

60. Model design for individual based stochastic simulations
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).
Probability
Distance
Household
Network
(disease specific)
Spatial

61. Spatial kernels – mobile phone data – frequency versus – distanced moved per defined time unit
Number of people
Distance metres

62. 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

63. 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 (

64. Eradication criterion – protective vaccines
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

65. 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.

66. 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

67. 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).
Vaccination & good outcome
of increased HIV-1 infection
but increased 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 decreased HIV-1 infection
& increased population size
(yv*<y*, Nv*>N*)
No persistence
of HIV-1 infection
(Ro<1)
Vaccination & eradication
of HIV-1 infection
(yv*=0)
No vaccination & endemic persistence
of HIV-1 infection
(Ro>1, p=0)