What drives antigenic drift in a single influenza season?

1. What drives antigenic drift in a single influenza season? Maciej F. BoniStanford University, Department of Biological SciencesCo-authors: Julia R. Gog, Viggo Andreasen, Marcus W. Feldman DIMACS Workshop on the Epidemiology and Evolution of Influenza Rutgers University, January 26, 2006

2. Strains have accumulated mutations. But how many? epidemic strain NOV APR Flu epidemics and antigenic drift weekly illnesses/10,000 inhabitants (NL) 20 ( focus will be on HA1 ) 1996 1997 1998 de Jong et al (2000)

3. 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)

4. Number of infections with epidemic-originating strain Number of infections with a strain k mutations away Neutral Epidemic Model

5. Exiting a population class via mutation Neutral Epidemic Model

6. Strain frequencies are Poisson-distributed Frequency of strain k: Mean number of mutations per virus moves forward in time according to a “molecular clock.”

7. 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

8. 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:

9. 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 )

10. j+kis distance between immunizing and challenging (infecting) strain Keeping track of hosts

11. infectivity reduction by previous infection with a strain j amino acids away force of infection of strain k total force of infection Keeping track of variables

12. Equations

13. total immunity in population cross-immunity between strains mamino acids apart Equations

14. mean fitness of strain population: W Equations fitness of strain k

15. Fisher’s Fundamental Theorem Population genetics 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.

16. Under neutrality

17. Takes 7 aa-changes to escape 50% immunity I(t)

18. Define the excess antigenic drift as: How do you know when the epidemic ends?

19. I(t)

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

21. Partial correlations immunity : immune-escape/mutation :

22. Partial correlations immunity : immune-escape/mutation :

23. Host immunity drives antigenic drift

24. 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.

25. 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 )