Transcript What Drives Antigenic Drift in Single Influenza Season?

What drives antigenic drift in a single influenza season?
Maciej F. Boni
Stanford University, Department of Biological Sciences
Co-authors: Julia R. Gog, Viggo Andreasen, Marcus W. Feldman
DIMACS Workshop on the Epidemiology and Evolution of Influenza
Rutgers University, January 26, 2006
Flu epidemics and antigenic drift
weekly illnesses/10,000 inhabitants (NL)
20
Strains have accumulated mutations.
But how many?
epidemic strain
( focus will be on HA1 )
1996
1997
NOV
1998
APR
de Jong et al (2000)
HA1 polymorphism – local datasets
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Coiras et al, Arch. Vir. (2001)
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Schweiger et al, Med. Microbiol. Immunol. (2002)
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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 crossimmunity.
We model this as an infectivity reduction
and say it wanes exponentially with
distance:
Non-neutral model
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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
q30
completely immune ( to I0 )
completely naive
j+k is distance between immunizing and challenging (infecting) strain
Keeping track of variables
infectivity reduction by previous infection
with a strain j amino acids away
force of infection of strain k
total force of infection
Equations
Equations
total immunity in population
cross-immunity between strains m amino acids apart
Equations
fitness of strain k
mean fitness of
strain population: W
Population genetics
Fisher’s Fundamental Theorem
Define mean antigenic drift in virus population as:
This is the Price Equation, thus, the basic influenza population dynamics
can 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
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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 Andreasen
University of Roskile, Department of Mathematics and Physics
Julia Gog
Cambridge University, Department of Zoology
Marc Feldman
Stanford University, Department of Biological Sciences
Freddy Christiansen
University of Aarhus, Department of Biology
Mike Macpherson
Stanford University, Department of Biological Sciences
( and for funding to NIH grant GM28016, NSF, and Stanford University )