1. Influenza Vaccination Strategies when supply is limited Romarie “Romie” Morales Rosado

2. Questions What is the impact of having access only to a limited number of dosages? What is the impact of delays in accessing the available vaccine supply? What is the role of a large percentage of H1N1 asymptomatic infectious individuals?

3. Type A and its subtypes Subdivided (H1-H16), (N1-N9)

4. Influenza virus and transmission http://www.youtube.com/watch?v=FvEOj wUOzJc

5. Impact Pandemic Influenza Source:http://commons.wikimedia.org/wiki/File:H1N1_map_by_confirmed_cases.svg WHO declared a pandemic in June 2009, a total of 74 countries and territories had reported laboratory confirmed infections. To date, most countries in the world have confirmed infections from the new virus.

6. Confirmed Deaths and Infections Source: http://commons.wikimedia.org/wiki/File:H1N1_map.svg

7. Pandemic 2009 vs. Pandemic 1918-19 Some similarities… Virus began to appear in the spring. Came out of nowhere…! Primarily attack young adults Elderly were partially immune to 2009 disease Source:http://news.sciencemag.org/sciencenow/2010/03/swine-flu-pandemic-reincarnates-.html?rss=1, http://ent.about.com/od/entdisordersgi/a/H1N1pandemic.htm

8. Prevention Methods

9. Methods of Prevention

10. Importance of Vaccination? Problem: Not enough vaccines for everyone Time constraint from identifying virus to creating and approving vaccine Rich-Poor country Division

11. Transmission Model V V P P S S F F J J R R E E I I D D Source: G. Chowell et al Addative vaccination strategies

12. System of nonlinear differential equations

13. Basic Reproductive Number

14. Parameters Source: G. Chowell et al Transmission dynamics of the great influenza pandemic of 1918 in Geneva, Switzerland R. Gani, H. Hughes, D. Fleming, T. Grifin, J. Medlock, S. Leach. Potential impact of antiviral use during influenza pandemic. Emerg Infect Dis; 11( 2005); 1355–362. I.M.LonginiJr.,M.E.Halloran,A.NizamandY.Yang.Containingpandemicinfluenzawithantiviralagents. American Journal of Epidemiology; 159(2004); 623–633. C.E. Mills, J.M. Robins and M. Lipsitch. Transmissibility of 1918 pandemic influenza. Nature 432 (2004):904–906.

15. Cases of Optimal Vaccine Strategies Limited Vaccine Access Almost unlimited Vaccine Access Time Delay

16. Optimal Control Problem L1 Set of functions –integral of function has finite solution we want u to belong to this set

17. Unconstraint Vaccine supply case

18. Sensitivity Analysis Weight Constant Control Upper Bound (maximum vaccination rate) Efficacy of Vaccine

19. Weight constant

20. Final epidemic Size when varying Weight Constant

21. Control upper bound on Final Epidemic Size

22. Vaccine Efficacy

23. Isoperimetric Constraint

24. Recap on Results Best to apply vaccines at the beginning of the transmission When transmission is weak a low vaccination policy is effective.

25. Initial conditions with Delay when R 0 = 1.3 R0=1.3 Delay =10 days Delay = 20 days Delay = 30 days S172810168750160820 V000 F000 P000 E4479491786 I2555451044 J109235456 R1387450610851 D72457 IC1758531112408 C000

26. Delay R 0 = 1.3

27. Initial conditions with Delay when R 0 =2 R0=2 Run= 10 days Run= 20 days Run=30 days S16780011931052110 V000 F000 P000 E2329133868916 I114373796517 J43430393313 R329131739103600 D16161551 IC488542318113980 C000

28. Delay R 0 = 2

29. Results Maximum Vaccination rate should be applied in a timely manner!!! No significant difference between unconstrained and constrained cases when R 0 is low (1.3) Increase in vaccine efficacy and upper bound of control results in a decrease in the amount of vaccines that must be administered Delay has impact on vaccine efficacy.

30. Future Work Include asymptomatic class and understand the impact of these individuals on disease transmission.