Carlos Castillo-Chavez Joaquin Bustoz Jr. Professor Arizona State University August 22, 2005

1. Carlos Castillo-Chavez Joaquin Bustoz Jr. Professor Arizona State University August 22, 2005 The role of crossimmunity on influenza dynamics Mathematical Modeling of Infectious Diseases: Dynamics and Control (15 Aug - 9 Oct 2005) Jointly organized by Institute for Mathematical Sciences, National University of Singapore and Regional Emerging Diseases Intervention (REDI) Centre, Singapore http://www.ims.nus.edu.sg/Programs/infectiousdiseases/index.htm Arizona State University

2. Recent work: Joint with Miriam Nuno, Harvard School of Public Health Zhilan Feng, Purdue University Maia Martcheva, University of Florida Arizona State University

3. Impact of Influenza Epidemics/Pandemics • 1918Spanish Flu (H1N1): 20% - 40% illness, 20 million deaths. • 1957 Asian Flu (H2N2): 70,000 deaths in US. • 1968 Hong Kong Flu (H3N2): 34,000 deaths in US. • 1976 Swine Flu Scare (H1N1 related??) • 1977 Russian Flu Scare (H1N1 related) • 1997 Avian Flu Scare (H5N1, human human) Arizona State University

4. Borrowed from Mac Hyman Arizona State University

5. Arizona State University THE DIFFUSION OF INFLENZA, Patterns and Paradigms, by Gerald F. Pyle

6. St = -lS + .k S It = lS + .kI l = r b(x,t,t) I/(S + I) k = mobility of the population The pandemic of 1781-82 originated in the Orient. Arizona State University THE DIFFUSION OF INFLENZA, Patterns and Paradigms, by Gerald F. Pyle

7. The pandemic of 1847-48 started in the Orient. In this epidemic, the diffusion pathways within western Europe changed after the railroads began running. Arizona State University THE DIFFUSION OF INFLENZA, Patterns and Paradigms, by Gerald F. Pyle

8. Diffusion Pathways for Primary Outbreaks of influenza Pandemic of 1918-19 Arizona State University THE DIFFUSION OF INFLENZA, Patterns and Paradigms, by Gerald F. Pyle

9. Diffusion Pathways for Primary Outbreaks of influenza Core Areas and During the Beginning of the 1967-68 Season THE DIFFUSION OF INFLENZA, Patterns and Paradigms, by Gerald F. Pyle Arizona State University

10. Core Areas and Diffusion Pathways for Primary Outbreaks of Influenza During the Beginning of the 1968-69 Season Susceptibility of the population is different for the second flu season of the same virus. Arizona State University THE DIFFUSION OF INFLENZA, Patterns and Paradigms, by Gerald F. Pyle

11. Weighted Network Nodes are cities weighted by their population. Edges are weighted by the mobility of people between the cities Arizona State University THE DIFFUSION OF INFLENZA, Patterns and Paradigms, by Gerald F. Pyle

12. Work of Mac Hyman and Tara La Force Arizona State University

13. Flow of people through a SIRP model with return to susceptibility S S P I I R R SIR Model with Loss of Immunity • Flow of people through a simple SIR model Partially Immune Susceptible Recovered Immune Infected Joint research with Tara LaForce Arizona State University

14. Mobility S P S P I R I R P S S P I R I R City 3 City 1 m13 m31 City 2 Arizona State University City 4

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17. Comparison of model and data for upper respiratory track illness The URT Data is rough compared with the smooth model predictions Y axis is in 100s of people/week infected. Arizona State University

18. Comparison of model and data for upper respiratory track illness Arizona State University

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22. End Work of Mac Hyman and Tara La Force Arizona State University

23. Motivation Researchers have explored the possible mechanism(s) underlying the recurrence of epidemics and persistence of co-circulating virus strains of influenza types between pandemics. We (CHALL I and II) began to explore role of cross-immunity in 1988 with the aid of mathematical models JMB Paper 1988: Castillo-Chavez, Hethcote, Andreasen, Levin and Liu Arizona State University

24. Influenza A reemerges year after year, despite the fact that infection leads to lifetime immunity to a strain Arizona State University

25. Modeling the Dynamics of Two-Strain Influenza Strains with Isolation and Partial Cross-Immunity • Previous Results (CHAL I and II, plus): • Herd-immunity, cross-immunity and age-structure are possible factors supporting influenza strain coexistence and/or disease oscillations • Set up: • We put two-influenza strains under various levels of (interference) competition with isolation periods and cross-immunity Some New Results (SIAM 2005 (Vol. 65: 3, 962-982) and …) • We establish that cross-immunity and host isolation lead to period epidemic outbreaks (sustained oscillations) where the periods of oscillations mimic those in real data • Multiple coexistence of strains even under sub-threshold conditions • Oscillatory coexistence is established via Hopf-bifurcation theory and numerical simulations using realistic parameter values Arizona State University

26. The Reservoirs of Influenza A Viruses Aquatic birds reservoir of all 15 subtypes of influenza A viruses Pigs are suspected to be the mixing vessel for influenza viruses Transmission of flu virus has been shown between pigs and humans People, pigs and aquatic birds main variables associated with interspeciestransfer of flu and emergence of new human pandemic strains Arizona State University Figure modified from : Microbiological Reviews, March ,1992, pp 152-179

27. Emergence and Reemergence of “New” Influenza A Virus in Humans • Molecular changes associated with emergence of a highly pathogenic H5N2 influenza virus in chicken in Mexico • In 1994 H5N2 (pathogenic) in Mexican chickens related to H5N2 isolated in shorebirds (Delaware Bay, US, • These H5N2 isolates replicated, spread rapidly and were not highly pathogenic. • However, in 1995 virus became highly pathogenic and HA acquired an • insert of 2 basic amino acids (Arg-Lys) possibly due to recombination and • a mutation. • The emergence of H5N1 influenza in Hong Kong • H5N1 (nonpathogenic) flu could have spread from migrating shorebirds • to ducks by fecal contamination of water. • The virus was transmitted to chickens and became established in live • bird markets in Hong Kong. During transmission between different species, • the virus became highly pathogenic for chickens • and occasionally was transmitted to humans from chickens in the markets. • Despite high pathogenicity for chickens (and humans), H5N1 were • nonpathogenic for ducks and geese. Arizona State University Pathogenic: Capable of causing disease

28. Schematic Model for Influenza Virus Particles The 8 influenza A viral RNA segments encode 10 recognized gene products (PB1,PB2, and PA polymerases, HA, NP, NA, M1 and M2 proteins, and NS1 and NS2 proteins. Surface proteins HA (hemagglutinin) and NA (neuraminidase) are the principal targets of the humoral immune response (i.e. response involving antibodies). Arizona State University Figure: Modified w/permission from H.N. Eisen and Lippincott-Raven, Microbiology, Fourth Ed., J.B. Lippincott Company, Philadelphia, 1990

29. Influenza type A H2N2 H1N1 H1N1 H3N2 Influenza Strains and Subtypes andthe role of Cross-immunity • Little evidence support the existence of cross-immunity between influenza A subtypes • Houston and Seattle studies show that cross-immunity exists between strains within the same subtype. Arizona State University

30. Influenza Epidemiology • Antigenic drift (resulting in minor yearly epidemics) • Antigenic shift (resulting in major epidemics with periods of ~ 27 years) • Seasonal occurrence • Low transmission rates out-of-season • Explosive onset of epidemics • Rapid termination of epidemics despite the continued abundance of susceptibles (Tacker) • Highest attack rates observed among children • Highest risk group observed in the elderly Arizona State University

31. What is Cross-Immunity? Infection with an influenza subtype A strain may provide cross protection against other antigenically similar circulating strains. Arizona State University

32. Experimental Evidence of Cross-immunity (1) • 1974:Study shows <3% with prior exposure to • A/Hong Kong/68 (H3N2) OR • A PRIOR A/ENGLAND/72 (H3N2) • GOTA/Port Chalmers/73 • VS • 23% with NO prior experience got infected • 1976:Appearance of A/Victoria/75 (H3N2) • Relative Frequency of First Infected/Previously Infected • (By another strain of H3N2 subtype was approximately 41%) • 1977:Co-circulating H1N2 strains • Individuals born before 1952 “GOT” a strain of H1N1 • Detection of antibody-positive sera • YOUNG: Changed from 0% to 9% • OLDER: Did not changed (remained at 9%) Arizona State University

33. Experimental Evidence of Cross-immunity (2) 1979:Christ’s Hospital study shows that past infection with H1N1 protected 55%. Protection (%): (Rate in ‘susceptibles’-Rate in ‘immunes)X100 Rate in ‘susceptibles’ 1982:(Glezen) No cross-immunity between subtypes H1N1 & H3N2 Arizona State University

34. Couch and Kasel (1983)Cross-immunity • Experimental results indicate that cross-immunity • shares the following features: • Exhibits subtype specificity • Exhibits cross-reactivity to variants within a subtype, but • with reduced cross-reactivity for variants that are • antigenically distant from the initial variant. • Exhibits a duration of at least five to eight years • Be able to account for the observation that resistance to • re-infection with H1N1 may last 20 years Arizona State University

35. Modeling Cross Immunity • -coefficient of cross-immunity • Relative reduction on susceptibility due to prior exposure to a related strain. • =0, represents total cross-immunity • =1, represents no cross-immunity • 0<<1, represents partial cross-immunity • >1, represents immune deficiency Arizona State University

36. Early Modeling Approaches • In 1975 epidemiological interference of virus populations was introduced [Dietz]. • In 1989 age-structure, proportionate mixing and cross- immunity are studied [Castillo-Chavez, et.al]. • In 1989 interactions between human and animal host populations are studied as a source of recombinants in strains and cross-immunity. Arizona State University

37. Basic Epidemiological Models: SIR Susceptible - Infected - Recovered Arizona State University

38. R S I S(t): susceptible at time t I(t): infected assumed infectious at time t R(t): recovered, permanently immune N: Total population size (S+I+R) Arizona State University

39. SIR - Equations Parameters Arizona State University

40. SIR - Model (Invasion) Arizona State University

41. Establishment of a Critical Mass of Infectives!Ro >1 implies growth while Ro<1 extinction. Arizona State University

42. Phase Portraits Arizona State University

43. SIR Transcritical Bifurcation unstable Arizona State University

44. Models without population structure Arizona State University

45. Ro “Number of secondary infections generated by a “typical” infectious individual in a population of mostly susceptibles at a demographic steady state Ro<1 No epidemic Ro>1 Epidemic Arizona State University

46. Ro = 2 Arizona State University

47. Ro = 2 Arizona State University

48. Ro = 2 ( End ) Arizona State University

49. Ro < 1 Arizona State University

50. Ro < 1 Arizona State University