The role of cross-immunity and vaccines on the survival of less fit flu-strains Miriam Nuño Harvard School of Public Health Gerardo Chowell Los Alamos National Laboratory Xiaohong Wang, Carlos Castillo-Chavez Arizona State University

Flu Epidemic and Pandemic Events 1918 Spanish Flu (H1N1): 500,000 deaths in US and 20 million worldwide Asian Flu (H2N2): 70,000 deaths in US Hong Kong Flu (H3N2): 34,000 deaths in US Swine Flu Scare (H1N1 related??) 1977 Russian Flu Scare (H1N1 related) 1997 Avian Flu Scare (H5N1, human human)

Aquatic birds reservoir of all 15 subtypes of influenza A viruses Pigs are suspected to be the mixing vessel for influenza viruses People, pigs and aquatic birds main variables associated with interspecies transfer of flu and emergence of new human pandemic strains Transmission of flu virus has been shown between pigs and humans The Reservoirs of Influenza A Viruses

What characterizes a successful invader? The establishment of an existing strain Quarantine The role of cross-immunity  The likelihood of coexistence  Phenotypic diversity  Invasion under sub-threshold condition

Cross-immunity? Infection with an influenza subtype A strain may provide cross protection against other antigenically similar circulating strains H1N1 H2N2 Influenza type A H1N1H3N2  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.

Experimental Evidence of cross-immunity

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 change (remained at 9%) 1982 (Glezen) No Cross-Immunity Between Subtypes (H1N1 & H3N2) Experimental Evidence of cross-immunity

Exhibits subtype specificity Exhibits cross-reactivity to variants within a subtype, but with reduced cross-reactivity for variants that are anti- genically 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 Cross-immunity Summarized

Model

Measure of the average reduced susceptibility to Strain j gained by a host after recovery with Strain i. 0 total immunity (strain j cannot invade) (0,1) intermediate immunity ( strain j likely invade ) 1 no immunity (strain j likely invade) 1 + immune deficiency (case not considered here) Cross-immunity in the model ( )

Flu Invasion Conditions (Nuño et al.,) Pathogen’s invasion determined by where, the mean transmission rate for Strain i is denoted by while describes the mean infectious period of strain i. Invasion of a fully susceptible population is ONLY possible when

Flu Invasion and Coexistence measures the ability of strain 2 to invade a strain- 1 endemic population 1 2  Number of secondary cases that strain-2 infected individuals generate in the susceptible fraction (primary infection) Number of secondary cases generated by strain-2 infected individuals among the partially immune proportion (secondary infection)

Uncertainty and Sensitivity Analysis of the Invasion Reproductive Number 1 2  Uncertainty analysis of quantities its variability generated from the uncertainty of the input parameters in (1). 1 2  Sensitivity Analysis evaluates the relative impact of to changes in the parameters in (1). 1 2  (1)

Model Parameters and Distributions

Uncertainty Analysis

Sensitivity Analysis

Contribution of to Coexistence 1 2 

Immune-specific Contributions to Coexistence

Estimation of the Contribution of to Coexistence: 1 2 

1 2 

Conclusions & Future Direction Invasion and coexistence are possible when the level of cross-immunity is moderate, even under sub-threshold condition. Cross-immunity reduces the likelihood of invasion. Transmission rate is the most sensitive parameter in (positively correlated) Study the role of quarantine on invasion and coexistence 1 2 

Acknowledgement NIH, NSF, MTBI and SAMSI