What drives antigenic drift in a single influenza season?

Maciej F. BoniStanford University, Department of Biological Sciences

Co-authors: Julia R. Gog, Viggo Andreasen, Marcus W. Feldman

DIMACS Workshop on the Epidemiology and Evolution of InfluenzaRutgers University, January 26, 2006

Flu epidemics and antigenic drift

1996 1997 1998

20

weekly illnesses/10,000 inhabitants (NL)

NOV APR

epidemic strain

de Jong et al (2000)

Strains have accumulated mutations. But how many?

( focus will be on HA1 )

HA1 polymorphism – local datasets

Coiras et al, Arch. Vir. (2001)

Schweiger et al, Med. Microbiol. Immunol. (2002)

Pyhälä et al, J. Med. Virol. (2004)

mean within-season distance = 2.8 aa (6nt)max within-season distance = 8 aa (25nt)

Neutral Epidemic Model

Number of infections with epidemic-originating strain

Number of infections with a strain k mutations away

Neutral Epidemic Model

Exiting a population class via mutation

Strain frequencies are Poisson-distributed

Frequency of strain k :

Mean number of mutations per virus moves forward in time according to a “molecular clock.”

Modeling antigenic drift and immunity

the epidemic-originating strain

-2 -1 0 1 2 3 4

you may have conferred immunity from a previous season to one of these strains.

Modeling antigenic drift and immunity

the epidemic-originating strain

-2 -1 0 1 2 3 4

Distance between immunizing strain and challenging strain determines level of cross-immunity.

We model this as an infectivity reduction and say it wanes exponentially with distance:

Non-neutral model

Amino-acid replacements in influenza surface proteins confer a fitness benefit via increased transmissibility

Hosts have some immunity structure from vaccination or previous infections

( need both )

Keeping track of hosts

q0 completely immune ( to I0 )

q30 completely naive

j+k is distance between immunizing and challenging (infecting) strain

Keeping track of variables

infectivity reduction by previous infectionwith a strain j amino acids away

force of infection of strain k

total force of infection

Equations

Equations

cross-immunity between strains m amino acids apart

total immunity in population

Equations

fitness of strain k

mean fitness of strain population: W

Population genetics

Define mean antigenic drift in virus population as:

Fisher’s Fundamental Theorem

This is the Price Equation, thus, the basic influenza population dynamicscan be viewed in a standard population genetic framework.

Under neutrality

I(t)

Takes 7 aa-changes to escape 50% immunity

Define the excess antigenic drift as:

How do you know when the epidemic ends?

I(t)

In general, how do the parameters affect the model results?

Partial correlations

immunity :

immune-escape/mutation :

Partial correlations

immunity :

immune-escape/mutation :

Host immunity drives antigenic drift

Public health implications

Vaccination strategies: under-vaccination or imperfect vaccination may cause much excess antigenic drift.

Pandemic implications: need to consider the effects of vaccination during the 2nd year after a pandemic, and their effects on the 3rd year after a pandemic.

Thanks

Viggo AndreasenUniversity of Roskile, Department of Mathematics and Physics

Julia GogCambridge University, Department of Zoology

Marc FeldmanStanford University, Department of Biological Sciences

Freddy ChristiansenUniversity of Aarhus, Department of Biology

Mike MacphersonStanford University, Department of Biological Sciences

( and for funding to NIH grant GM28016, NSF, and Stanford University )