Pathogen adaptation under imperfect
vaccination: implications for pertussis
Michiel van Boven1, Frits Mooi2,3, Hester de Melker3
Joop Schellekens3 & Mirjam Kretzschmar3
1Wageningen
University/Utrecht University
2Utrecht University/Academic Hospital Utrecht
3National Institute of Public Health & the Environment
Pertussis, basic facts

gram-negative bacterium

first described: 1540 !

first isolated: 1906 by Bordet and Gengou

main species in the genus Bordetella: B. pertussis,
B. parapertussis, and B. bronchiseptica

B. pertussis and B. parapertussis : mostly human

B. bronchiseptica : dogs, pigs, sheep

Bp and Bpp : limited survival outside the host

Bb : prolonged starvation resistance

Bp and Bpp infections: severe in unvaccinated infants,
usually mild in adolescents and adults
Pertussis vaccination

before 1940: a leading cause of infant death

nowadays: very low mortality rates in developed countries

Dutch vaccination program: started in 1953

vaccine: killed whole-cell (Tohama)

vaccination coverage: ~96%

up to 2002: vaccination at age 3,4,5, and 11 months

since 2002: vaccination at age 2,3,4, and 10 months

since 2002: booster with subunit vaccine at 4 years

2006: replacement of whole-cell vaccine by subunit vaccine

subunit vaccines: 1-5 components (e.g., ptx, pertactin, fha)
-1
number of cases (month )
Pertussis trend in the Netherlands
1000
800
600
400
200
0
1/1990
1/1992
1/1994
1/1996
date
1/1998
1/2000
1/2002
Age distribution of cases before and after 1996
Distribution of cases by vaccination status
Virulence genes of B. pertussis
Phase modulation in the bordetellae
Questions



What is the contribution of circulation in unvaccinated
infants to the overall circulation of pertussis?
How does the infection incidence depend on period of
immunity after vaccination or infection?
How will the pathogen population evolve in response to
vaccination?
Model structure
1-p
p
g 1h
V
I1
gVh
V
S2
S1
a1
g2 h
I2
a2
R
Central idea: there is a
difference between
infection in immunologically
naïve individuals (‘primary
infection’) and infection in
individuals whose immune
system has been primed
(‘secondary infection’)
Model parameters
Population dynamical analysis: invasion
f 1g 1
σV f 2 g 2
Rp  1 - p
p
α1  μ
σV  μ α 2  μ

herd immunity cannot always be achieved (McLean and others)
f 2 g 2 σV  μ

 the reproduction ratio increases with p if
f 1g1
σV

for the default parameter values, Rp increases with p if
secondary infections are 7% more transmissible than primary
infections
Population dynamical analysis: endemicity
Evolutionary adaptation
Adaptation of B. pertussis to
vaccination occurs in two ways:
(1) the pathogen population may
evolve to become polymorphic
(2) the pathogen may evolve
higher or lower levels of
virulence gene expression
Scenarios
1.
B. pertussis can increase (or decrease) its efficiency in
immunologically naïve individuals by increasing (decreasing) the
expression of virulence genes. On the other hand, increased
expression of virulence genes results in a stronger immune
response in primed individuals.
2.
B. pertussis can evolve to circumvent the immunity induced by
vaccination. However, strains that circumvent the vaccination
induced immune response have reduced fitness.
Evolutionary invasion analysis

fitness measure: the growth rate λ(y,x) of a mutant strain
characterized by a variable y in a resident pathogen
population characterized by a variable x

the selection gradient:

ESS condition:

maximum condition:

convergence condition:
1. virulence gene expression
In the first example, the parameters f1 and f2 are
molded by selection.
 For this scenario, the ESS condition reads

S1 f1 
df 2

df 1 f1 f1 S2 f1   gVV f1 
1. virulence gene expression
1. virulence gene expression
trade-off: f 2  250  1 f 1 2
250
2. immune evasion

In this example, the parameters σV and α are
supposed to be molded by selection, and the
ESS condition reads
dα
dgV
 f2V gV   f2
gV  gV
μ
p
μ  σV  gV h gV 
2. immune evasion




Suppose that a resident strain is present that cannot
infect individuals in class V (gv=0)
The infectious period of the resident strain is
1
365  14.6 days.
α μ
A mutant strain that is fully able to infect individuals in
class V (i.e. g’v=0) can invade if its infectious period is
1
not shorter than
365  13.1 days.
α  μ  Δα
If the period of protection after vaccination is ten years
(instead of five), the mutant can invade the infectious
1
period is not shorter than
365  11.9 days.
α  μ  Δα
Pathogen adaptation: summary of results



For realistic parameter values primary susceptibles
constitute only a small fraction of the population, while
secondary susceptibles abound. Consequently, pertussis
circulation depends mainly on (unnoticed) infections in
children, adolescents and adults.
The pathogen is more likely to adapt to efficiently exploit
secondary susceptibles than to efficiently exploit primary
susceptibles.
Pertussis strains that evade the immunity induced by
vaccination can only invade if they incur no or a modest
fitness cost.
Tests and open questions


How long does immunity, against infection and against
disease, last after infection and vaccination?
Are there systematic differences between strains found
in countries with high vaccination coverage and strains
found in countries with low vaccination coverage?
The optimal amount of antiviral control
Michiel van Boven1, Don Klinkenberg1, Franjo Weissing2, Hans Heesterbeek1
1Faculty
of Veterinary Medicine, Utrecht University
2Theoretical
Biology, University of Groningen
Main question: What is the optimal amount
of costly (i.e. potentially lethal) antiviral
therapy when faced with a virulent
pathogen that can kill the host?
Two perspectives

the public health officer: maximize the
performance of the population

the individual: maximize your own performance
given the actions of those around you
Objective functions

life expectancy, L(y,x)

probability to be alive after T years, L(y,x,T)

perceived risk, L(y, I(x), V(x))
Model structure
μ : background mortality
ρ : recovery rate
γ : antivirals induced mortality
ν : antiviral control rate
α : infection induced mortality
σ: non-compliance rate
 : force of infection
1. Life expectancy at the endemic equilibrium

pathogen absent:

no antiviral control:

no individual differences:

rare type νy in a resident population νx :
Endemic pathogens, life expectancy as objective function
Endemic pathogens, life expectancy as objective function
Endemic pathogens, limited time horizon
Endemic pathogens, limited time horizon
Outbreak situations, limited time horizon
?