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**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

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**Contents-Lecture 1 History. Basic epidemiological principles.**

Criteria for eradication. Heterogeneities. Impact of mass vaccination on epidemiological pattern. Conclusions. Epidemic curves

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**Vaccines as a fraction of total **

pharmaceutical sales in total â€“ worldwide in 2006 Total sales - $ 380 billion

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**Geographical distribution of vaccine market share April 2011**

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**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 â€“ of the order of 10 years or longer

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**Measles â€“ England & Wales**

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**Pertussis notifications â€“ England & Wales**

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**Emergence of P3 strains of Bordetella pertussis**

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**Sero-surveillance â€“ mumps - Netherlands**

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**Hib (Haemophilus influenzae type b) Vaccination â€“ England & Wales**

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**Pneumococcal disease age distribution - Netherlands**

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**Basic epidemiological principles**

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**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.

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**Critical community size**

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

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**Seasonality in transmission of measles â€“ school holidays**

Confidence bar

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**HIV-1 prevalence in Nairobi, Kenya 1981-1999 â€“ stratified by risk group**

% infected with HIV-1 Sex workers Men with GUD Pregnant women Sex workers Men with GUD Pregnant women Year

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**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).

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**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.

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**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.

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**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 ï‚µ e(R0-1)/TG t Random (stochastic) effects

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**Typical course of infection within the host**

Estimation of average latent & infectious periods plus distributions

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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 TCID50ï‚´h/mL) 500 400 300 200 100 10 20 30 40 50 60 70 80 Age (years) 90 100

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**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)

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**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.

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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.

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**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.

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**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.

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**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

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

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**Force or rate of infection Î» and the average age of infection A â€“ estimation from serology (1)**

If the proportion seropositive at age a is p(a), then the average force or rate of infection Î» over the interval 0 to a years of age is given by: Î»(a)=p(a)/[L(1-e(-a/L))]; eq(1) where L is life expectancy. Other relationships of importance are: Aâ‰ˆ1/Î»; eq(2) R0â‰ˆL/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.

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**Force or rate of infection Î» and the average age of infection A â€“ 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) Î» = 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 Î» â€“ which gives a required coverage of 94.2% (see Anderson & May (1991) for fuller discussion)

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**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

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**Force or rate of infection Î» and the average age of infection A â€“ 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

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**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

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Human Parvovirus B19 serology â€“ 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, 1059â€“1068 Belgium England Finland Poland % Seropositive Force of Infection (FOI) Italy Age (years)

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**Parameters â€“ 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, 936â€“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, 1158â€“1166. Edmunds WJ, Oâ€™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, 949â€“957. Farrington CP. (1990) Modelling forces of infection for measles, mumps and rubella. Statistics in Medicine 9, 953â€“967.

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**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

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**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

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**Estimation of R0 from past influenza A epidemics**

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**SARS - distribution of R**

Rapid SARS Virus Spread in Flats 7 and 8, Block E Amoy Garden, Hong Kong. 1st March 2003 â€“ 292 people infected by one index case Super spreading events (person, place & setting)

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**The generation of secondary cases with vaccination**

1 2 3 4 5 6 7 8 Number Infected R 1.5 1.33 1.25 0.2 Vaccinated individuals

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**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 = Îµ, ranging from 0-1.

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**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%

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**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

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**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

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**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

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**Average age of infection - the impact of vaccination**

prior to vaccination set at 5 years. Average age of vaccination set at 2 years.

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**Vaccination - and the age distribution of infection**

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**Impact of vaccination on serology**

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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

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**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

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**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

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**Percentage gain from the indirect effects of herd immunity**

Critical vaccination coverage to block transmission, pc

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**Ferguson et al, 2006 â€“ Nature - on line April 27th 2006**

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

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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 â€“ phase IV monitoring of vital importance. Multi- strain systems â€“ more research required â€“ will new strains replace those targeted by a multi-valent vaccine?

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The End

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**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.

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**Rubella vaccination programmes in the UK â€“ 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 â€“ 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

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**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.

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**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

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**Spatial kernels â€“ mobile phone data â€“ frequency versus â€“ distanced moved per defined time unit**

Number of people Distance metres

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

Need both population data (density, age, household) and mixing/travel data. Population density â€“ based on satellite imagery

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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 VaxGenâ€™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 (

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**Eradication criterion â€“ 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 Îµ is vaccine efficacy

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Imperfect vaccines Vaccinated individuals acquire infection but show slower progression to AIDS. Slower progression is linked to lower viral loads â€“ 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.

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**Eradication criterion â€“ 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 Îµ is vaccine efficacy

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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)

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