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Effects of heterogeneity in hosts and pathogens on effectiveness of vaccination Mirjam Kretzschmar RIVM, Department of Infectious Diseases Epidemiology The Netherlands Populations are heterogeneous ... Why do we have to think about heterogeneity?

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effects of heterogeneity in hosts and pathogens on effectiveness of vaccination

Effects of heterogeneity in hosts and pathogens on effectiveness of vaccination

Mirjam Kretzschmar

RIVM, Department of Infectious Diseases Epidemiology

The Netherlands

why do we have to think about heterogeneity
Why do we have to think about heterogeneity?

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

host heterogeneity
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
    • Clininal symptoms or asymptomatic
pathogen heterogeneity
Pathogen heterogeneity
  • Heterogeneity between strains:
    • Virulence (defined as host mortality or severity of disease)
    • Vulnarability to host immune response
    • Competition via cross-immunity
  • Within host heterogeneity:
    • Immunogenic variability (HIV)
    • Different location within host leads to different effects (invasive infection versus carrier)
effects of heterogeneity on vaccination depend on vaccination strategy
Effects of heterogeneity on vaccination depend on vaccination strategy
  • Universal vaccination
    • Rationale: create herd immunity such that unvaccinated individuals are also protected
      • pockets of not vaccinated persons (MMR vaccination in the Netherlands)
      • core groups of individuals with very many contacts (STD, Hepatitis B)
      • non-homogeneous contact patterns, i.e. household contacts, spatial patterns,
      • repeated contacts with same individuals (long term partnerships, networks)
Targetted vaccination of risk groups
    • Rationale: protect those individuals who are at greatest risk for being infected
      • Takes heterogeneity in risk into account, but what are effects of mixing between risk groups?
      • Critical coverage per risk group?
      • Effects of vaccination on non-risk groups?
Ring vaccination
    • Rationale: vaccinate direct contacts of infected individuals to interrupt transmission chain
      • Heterogeneity in contact patterns is taken into account, only persons at risk are included in vaccination.
      • But: how to estimate fraction of contacts that have been found and vaccinated?
      • Modelling: Contact tracing requires a network modelling approach
contact and transmission route
Contact and transmission route
  • Influenza (airborne infection):
    • talking with each other at close distance
    • coughing at each other
  • Gonorrhoea (sexually transmitted dis.):
    • sexual intercourse
  • Hepatitis C (bloodborne infection):
    • sharing contaminated needles
    • blood transfusion
knowledge about contact patterns leads to insight into transmission routes
Knowledge about contact patterns leads to insight into transmission routes
  • Contact network AIDS cases (Auerbach et al. 1984)
    • Probability that cluster of cases is connected by contact on the basis of random events
    • timing of contacts and onset of disease
  • Hypothesis: AIDS is transmitted by homosexual contact
cluster of aids patients
Cluster of AIDS patients

number: order of diagnosis

0 index case

A.S. Klovdahl. Social networks and the spread of infectious diseases:

The AIDS example. Soc. Sci. Med. 21 (1985): 1203-1216.

contacts are non random
  • Population heterogeneity
    • Age structure, social economic structure, education
  • Social grouping
    • Families, working environment, recreation
  • Geographical distribution
    • Cities, rural areas, mobility between regions

 People are not the same and they choose contacts with certain preferences

 these choices influence the way infectious diseases spread

influence of contact patterns on epidemiological outcome
Influence of contact patterns on epidemiological outcome
  • Age distribution of cases in STDs for men and women
  • Biannual measles epidemics in prevaccination era
  • High prevalence of STDs in high activity core groups
  • Widespread heterosexual transmission of HIV in sub-Saharan Africa
  • Hepatitis A outbreaks in day care centers
  • Increasing incidence of HIV in monogamous married women in Thailand
  • Increasing incidence of malaria in Western Europe
modelling heterogeneity
Modelling heterogeneity
  • Heterogeneity in number of contacts
    • Core groups
    • Stratification by activity
    • Mixing?
  • Local/global contacts
    • Households
    • Metapopulation models
  • Partnership duration: pair formation models, pair approximation models
  • Networks
vaccination in a population stratified by households
Vaccination in a population stratified by households

local contacts

global contacts

Equalizing strategy: Choose individuals for

vaccination sequentially from those households with largest number of susceptibles.

Minimizes the number of vaccinations needed to reduce R to below 1.

Ball, Mollison & Scalia-Tomba.Ann. Appl. Prob. 7 (1997) 46.

the basic reproduction number r 0
The basic reproduction number R0

The expected number of secondary cases caused by one index case during his entire infectious period in a completely susceptible population.

homogeneous population: R0=cD

heterogeneous population: number of secondary cases has to be averaged in the right way.

heterogeneous population
Heterogeneous population

Diekmann, Heesterbeek, Metz. J. Math. Biol. 1990; 28:365-382

Diekmann, Heesterbeek. Mathematical Epidemiology of Infectious Diseases, Wiley, 2000.

Next generation operator

Number of cases in the (n+1)-th generation of infections given the distribution of infectious individuals (with respect to population structure) in the n-th generation.

Basic reproduction number

Dominant eigenvalue of the next-generation operator

Explicit calculation of R0 for separable mixing

Contact funtion c(a,b)=f(a)g(b)

host heterogeneity example hepatitis b vaccination
Host heterogeneity: example Hepatitis B vaccination
  • Background:
    • Introduction of universal infant vaccination in the Netherlands?
    • Low prevalence, high costs of vaccination
    • How many cases of chronic hepatitis B infection can potentially be prevented?
  • Project including case-control study, modelling and cost-effectiveness analysis
hepatitis b many types of heterogeneity
Hepatitis B: many types of heterogeneity
  • Transmission routes:
    • Sexual transmission
    • Vertical to babies at birth
    • Horizontal close contact (household)
  • Age:
    • Age dependent immune response (clinical symptoms and development of chronic carrier state)
    • Age dependent sexual activity level
  • Behaviour:
    • High versus low activity within age groups
  • Disease states:
    • Latent (1-2 months), acute (3-4 months), and chronic stages







Model structureWilliams et al. (1996), Epidemiol & Infect. 116: 71-89Kretzschmar et al. (2002) Epidemiol & Infect. 128: 229-244.
  • Population stratified by age and sexual activity (6 activity classes)
  • Two transmission routes (vertical and sexual)
  • Different stages of infection (acute, chronic carrier)
  • System of partial differential equations (age structure)
  • Proportionate mixing
  • Separate models for hetero/homosexual populations
  • Included immigrationand age dependence in probability to become carrier
  • Explicit formula for R0
calculation of r 0
Calculation of R0

Individuals can be infected via two routes.

R0 is the dominant eigenvalue of next generation matrix

s sexual transmission

v vertical transmission

calculation of r 0 ss
Calculation of R0ss


  • L maximum lifetime
  • k fraction in activity class k =1,...6
  • ck(a) age dependent contact rate in activity class k
  • time since infection

i transmission probability per partnership

age dependence of becoming carrier
Age-dependence of becoming carrier

PC(,a) has factor p(a), the probability of becoming carrier

when infected at age a

for a=0

for a>0

Edmunds et al. 1993:

Point estimate of parameters 1 and 2 from data

from 29 different studies

estimate r 0
Estimate R0
  • Homosexual men R0>1:
    • Hepatitis B virus can persist
    • Immigration of infected persons has little influence
  • Heterosexual population R0<1:
    • short transmission chains
    • immigration of infected persons determines prevalence
compare with data
Compare with data
  • Case control study:
    • heterosexual cases (N=41): 60% of cases infected by immigrant from high endemic country
    • homosexual cases (N=44): 16% infected by immigrant from medium or high endemic country
conclusions for vaccination
Conclusions for vaccination
  • Vaccinating general population can reduce incidence of new infections within the country, but has little influence on prevalence of carriers.
  • Vaccination of risk groups is being intensified
  • Vaccination is offered to children of whom at least one parent is an immigrant from country with higher prevalence
vertical transmission
Vertical transmission
  • In highly endemic countries it is believed that vertical transmission and horizontal transmission to children are the most important transmission routes.
  • In low endemic countries the role of horizontal transmission to children is not known.
  • Can we use R0 to analyse importance of those transmission routes?
  • Assume sexual behaviour comparable to UK data
consider r 0 vv
Consider R0vv


() fertility rate at age 

bi transmission probabilities per offspring

(b1=0.724, b2=0.115)

horizontal transmission
Horizontal transmission
  • Horizontal transmission in households can be approximately described by increasing bi
  • The fertility function can vary in age distribution and total number of offspring during lifetime.
  • Example: mean offspring number 3, b2=0.5

R0 = 1.29

  • Neither of the transmission modes alone could sustain

endemic prevalence, together they can

  • Explicit expression for R0 in heterogeneous populations can help to get insight into influence of different types of heterogeneity on transmission dynamics and their interaction
  • Drawback: proportionate mixing assumption
  • How does R0 depend on underlying model assumptions?
  • How well does R0 reflect heterogeneity?
  • Hepatitis B: different vaccination strategies depending on population heterogeneity?
heterogeneity in the pathogen population and vaccination
Heterogeneity in the pathogen population and vaccination
  • When can serotype replacement occur?
  • Indirect effects of serotype replacement: partial immunisation by replacing strains?
  • Optimal composition of vaccine (trade-off between breadth and effectiveness)?
  • Evolution to higher virulence?
  • Vaccination against disease or against infection?
competition of 2 strains
Competition of 2 strains

Model McLean:


  • 2 strains, total cross-immunity
  • Vaccinated individuals can become infected with a small probability, vaccine efficacy differs between strains
  • after infection permanent immunity
  • Strain 1 outcompetes 2 in absence of vaccination

A.R. McLean. Proc R Soc Lond B (1995) 261: 389-393.

mclean model
McLean model














recovery + death

effects of vaccination
Effects of vaccination
  • Vaccination reduces competitive pressure on weaker strain 2 -> outbreaks
  • indirect effect: more herd immunity against strain 1

Model Lipsitch:


  • no immunity, after recovery susceptible again
  • Individual can be infected by 2 strains simultaneously
  • Cross-immunity
  • vaccine 100% effectiv for target strain

M. Lipsitch. Emerging Infectious Diseases (1999) 5: 336-345

model with superinfection
Model with superinfection



















effects of vaccination44
Effects of vaccination
  • Vaccination enables coexistence of strains
  • serotype replacement can occur
  • If vaccine is also effective for other than the target strains, higher coverage is needed for eradication
example pertussis
Example pertussis
  • Since middle of the 90‘s increase in incidence of pertussis in NL
  • Increase in incidence among vaccinated children
  • Large incidence of subclinical infections in adults
  • Hypothesis: vaccine not as effective against presently circulating strains
  • Full cross immunity after natural infection
  • vaccine protects fully against strain 1, partly against strain 2
  • vaccine induced immunity lasts shorter than natural immunity
  • Strains can coexist for certain range of vaccination coverage
  • for high coverages strain 2 is dominant
  • total prevalence of infection decreases with increasing coverage
  • elimination for p larger than critical vaccination coverage
  • For high coverages coexistence of both strains
  • total prevalence of infection increases when 2 strains are present
  • infection remains present even with 100% vaccination coverage
  • Vaccination can lead to coexistence of strains
  • Contribution of secondary infections determines success of vaccination
  • Even very high coverage might not suffice for elimination
  • Changes of transmission rate of primary infections may lead to sudden shifts in prevalence
  • Need more empirical data about secondary infections