Pathogen adaptation under imperfect vaccination: implications for pertussis Michiel van Boven 1, Frits Mooi 2,3, Hester de Melker 3 Joop Schellekens 3 & Mirjam Kretzschmar 3 1 Wageningen University/Utrecht University 2 Utrecht University/Academic Hospital Utrecht 3 National 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

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 g1hg1h gVhgVh     p 1-p g2hg2h VV

Model parameters

herd immunity cannot always be achieved (McLean and others) the reproduction ratio increases with p if for the default parameter values, R p increases with p if secondary infections are 7% more transmissible than primary infections Population dynamical analysis: invasion

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 In the first example, the parameters f 1 and f 2 are molded by selection. For this scenario, the ESS condition reads

1. virulence gene expression

trade-off: 1. virulence gene expression

2. immune evasion In this example, the parameters σ V 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 (g v =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.

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 Boven 1, Don Klinkenberg 1, Franjo Weissing 2, Hans Heesterbeek 1 1 Faculty of Veterinary Medicine, Utrecht University 2 Theoretical 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 ν y in a resident population ν x :

Endemic pathogens, life expectancy as objective function

Endemic pathogens, limited time horizon

Outbreak situations, limited time horizon ?