Effects of heterogeneity in hosts and pathogens on effectiveness of vaccination
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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 l.jpg

Effects of heterogeneity in hosts and pathogens on effectiveness of vaccination

Mirjam Kretzschmar

RIVM, Department of Infectious Diseases Epidemiology

The Netherlands


Populations are heterogeneous l.jpg
Populations are effectiveness of vaccinationheterogeneous ...


Why do we have to think about heterogeneity l.jpg
Why do we have to think about heterogeneity? effectiveness of vaccination

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


Host heterogeneity l.jpg
Host heterogeneity effectiveness of vaccination

  • 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 l.jpg
Pathogen heterogeneity effectiveness of vaccination

  • 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 l.jpg
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)


Slide7 l.jpg

  • Targetted vaccination of risk groups vaccination strategy

    • 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?


Slide8 l.jpg

  • Ring vaccination vaccination strategy

    • 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 l.jpg
Contact and transmission route vaccination strategy

  • 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 l.jpg
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 l.jpg
Cluster of AIDS patients transmission routes

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 l.jpg
Contacts transmission routesarenon-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 l.jpg
Influence of contact patterns on epidemiological outcome transmission routes

  • 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 l.jpg
Modelling heterogeneity transmission routes

  • 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 l.jpg
Vaccination in a population stratified by households transmission routes

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 l.jpg
The basic reproduction number R transmission routes0

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 l.jpg
Heterogeneous population transmission routes

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 l.jpg
Host heterogeneity: example Hepatitis B vaccination transmission routes

  • 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 l.jpg
Hepatitis B: many types of heterogeneity transmission routes

  • 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


Slide21 l.jpg

susceptible transmission routes

latent

acute

vaccinated

carrier

immune

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)


Model l.jpg
Model transmission routes

  • 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 l.jpg
Calculation of R transmission routes0

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 l.jpg
Calculation of R transmission routes0ss

with

  • 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 l.jpg
Age-dependence of becoming carrier transmission routes

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




Estimates for r 0 heterosexual population l.jpg
Estimates for R NL)0(heterosexual population)


Estimate r 0 l.jpg
Estimate R NL)0

  • 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 l.jpg
Compare with data NL)

  • 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 l.jpg
Conclusions for vaccination NL)

  • 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 l.jpg
Vertical transmission NL)

  • 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 l.jpg
Consider NL)R0vv

with

() fertility rate at age 

bi transmission probabilities per offspring

(b1=0.724, b2=0.115)



Horizontal transmission l.jpg
Horizontal transmission NL)

  • 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



Conclusions l.jpg
Conclusions NL)

  • 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 l.jpg
Heterogeneity in the pathogen population and vaccination NL)

  • 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 l.jpg
Competition of 2 strains NL)

Model McLean:

Assumptions:

  • 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 l.jpg
McLean model NL)

vaccination

birth

S

V

transmission

2I2S

death

death

1I1S

(1-r)2I2V

(1-s)1I1V

I1

I2

recovery + death


Effects of vaccination l.jpg
Effects of vaccination NL)

  • Vaccination reduces competitive pressure on weaker strain 2 -> outbreaks

  • indirect effect: more herd immunity against strain 1


Superinfection l.jpg
Superinfection NL)

Model Lipsitch:

Assumptions:

  • 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 l.jpg
Model with superinfection NL)

vaccination

birth

transmission

S

V

recovery

death

2(I2+I12)S

1(I1+I1v+I12)S

(1-s)1(I1+I1v+I12)V

I2

I1

I1v

I1v

c22(I2+I12)I1

c11(I1+I1v+I12)I2

I12

aI1I2


Effects of vaccination44 l.jpg
Effects of vaccination NL)

  • 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 l.jpg
Example pertussis NL)

  • 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



Assumptions l.jpg
Assumptions NL)

  • Full cross immunity after natural infection

  • vaccine protects fully against strain 1, partly against strain 2

  • vaccine induced immunity lasts shorter than natural immunity


Equilibrium under vaccination primary infection more transmissible r 0 1 r 0 2 l.jpg
Equilibrium under vaccination NL)primary infection more transmissible, R01>R02



Conclusions50 l.jpg
Conclusions NL)

  • 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


Equilibrium under vaccination secondary infection more transmissible l.jpg
Equilibrium under vaccination NL)secondary infection more transmissible



Conclusions53 l.jpg
Conclusions NL)

  • 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


Summary l.jpg
Summary NL)

  • 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


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