The role of cross-immunity and vaccines on the survival of less

fit flu-strainsMiriam Nuño

Harvard School of Public HealthGerardo Chowell

Los Alamos National LaboratoryXiaohong 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.

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)

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

H1N1H2N2

Influenza type A

H1N1 H3N2

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.

1974 Study < 3% With Prior A/HONG KONG/68 (H3N2) OR

A PRIOR A/ENGLAND/72 (H3N2)

GOT A/PORT CHALMERS/73

vs.

23% With NO Prior Experience

1976 Appearance of A/VICTORIA/75 (H3N2)Relative Frequency of First Infected/Previously Infected

(By Another Strain of H3N2 was approximately 59%)

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.

ij

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 ( )ij

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

),max( 210

ii

ii

iii

1

10

Flu Invasion and Coexistence

measures the ability of strain 2 to invade a strain-1 endemic population

12

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)

AS~

/~

1

AR~

/~

1

A

R

A

S~

~

~

~1

2

212

1

22

212

A

Snaive~

~1

22

22

A

Rimmunecross~

~1

2

2122

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).

12

Sensitivity Analysis evaluates the relative impact of to changesin the parameters in (1).

12

(1)

Model Parameters and Distributions

Uncertainty Analysis

.10 size ofeach samples 10for 1 exceeds that

y probabilit and of variancemean, for the Estimates51

2

12

0.3.mean ith immunity w-crossfor quantified

are 1)( ecoexistenc to and ofon contributi

The 10. of size sample with and for y probabilit

ingcorrespond and variancemean, for the estimates 10 of sMean value

12

immune-cross2

naive2

immune-cross2

naive2

.ssimulation Carlo Monte10 using )8.0,3.0( regimesimmunity

-cross separate for two of functionson distributi Cumulative5

ij

12

parameter.input each and and ,between

s)(PRCC' tscoefficienn correlatiorank partial Summarizedimmune-cross

2naive2

12

Sensitivity Analysis

Contribution of to Coexistence12

Immune-specific Contributions to Coexistence

Estimation of the Contribution of to Coexistence:12 8.012

Estimation of the Contribution of to Coexistence: 12 3.012

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

12

Acknowledgement

NIH, NSF, MTBI and SAMSI