Pathogen adaptation under imperfect vaccination: implications for pertussis

Michiel van Boven1, Frits Mooi2,3, Hester de Melker3

Joop Schellekens3 & Mirjam Kretzschmar3

1Wageningen University/Utrecht University2Utrecht 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)

Pertussis trend in the Netherlands

date1/1990 1/1992 1/1994 1/1996 1/1998 1/2000 1/2002

num

ber of

cas

es (m

onth-1

)

0

200

400

600

800

1000

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

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’)

S

V

S I R

I

1

1

22

g1h

gVh

p

1-p

g2h

V

Model parameters

herd immunity cannot always be achieved (McLean and others)

the reproduction ratio increases with p if

for the default parameter values, Rp increases with p if

secondary infections are 7% more transmissible than primary infections

Population dynamical analysis: invasion

V

V

σμσ

gfgf

11

22

μα

gfμσ

σp

μαgf

RV

V

2

22

1

11p p-1

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.

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:

Evolutionary invasion analysis

1. virulence gene expression

112

11

1

2

11fVgfS

fSdfdf

Vff

In the first example, the parameters f1 and f2 are

molded by selection. For this scenario, the ESS condition reads

1. virulence gene expression

trade-off: 212250

1250 ff

1. virulence gene expression

2. immune evasion

pghgσμ

μfgVf

dgαd

VVVV

ggVVV

22

In this example, the parameters σV and α are

supposed to be molded by selection, and the ESS condition reads

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 days. 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 not shorter than days. If the period of protection after vaccination is ten years (instead of five), the mutant can invade the infectious period is not shorter than days.

6.143651 μα

1.13365Δ

1 αμα

9.11365Δ

1 αμα

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?

Michiel van Boven1, Don Klinkenberg1, Franjo Weissing2, Hans Heesterbeek1

1Faculty of Veterinary Medicine, Utrecht University

2Theoretical Biology, University of Groningen

The optimal amount of antiviral control

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?

the public health officer: maximize the

performance of the population

the individual: maximize your own

performance

given the actions of those around you

Two perspectives

life expectancy, L(y,x)

probability to be alive after T years, L(y,x,T)

perceived risk, L(y, I(x), V(x))

Objective functions

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

?