Is population structure sufficient to generate area-level inequalities in influenza rates? An examination using agent-based models

Background In New Haven County, CT (NHC), influenza hospitalization rates have been shown to increase with census tract poverty in multiple influenza seasons. Though multiple factors have been hypothesized to cause these inequalities, including population structure, differential vaccine uptake, and differential access to healthcare, the impact of each in generating observed inequalities remains unknown. We can design interventions targeting factors with the greatest explanatory power if we quantify the proportion of observed inequalities that hypothesized factors are able to generate. Here, we ask if population structure is sufficient to generate the observed area-level inequalities in NHC. To our knowledge, this is the first use of simulation models to examine the causes of differential poverty-related influenza rates. Methods Using agent-based models with a census-informed, realistic representation of household size, age-structure, population density in NHC census tracts, and contact rates in workplaces, schools, households, and neighborhoods, we measured poverty-related differential influenza attack rates over the course of an epidemic with a 23 % overall clinical attack rate. We examined the role of asthma prevalence rates as well as individual contact rates and infection susceptibility in generating observed area-level influenza inequalities. Results Simulated attack rates (AR) among adults increased with census tract poverty level (F = 30.5; P < 0.001) in an epidemic caused by a virus similar to A (H1N1) pdm09. We detected a steeper, earlier influenza rate increase in high-poverty census tracts—a finding that we corroborate with a temporal analysis of NHC surveillance data during the 2009 H1N1 pandemic. The ratio of the simulated adult AR in the highest- to lowest-poverty tracts was 33 % of the ratio observed in surveillance data. Increasing individual contact rates in the neighborhood did not increase simulated area-level inequalities. When we modified individual susceptibility such that it was inversely proportional to household income, inequalities in AR between high- and low-poverty census tracts were comparable to those observed in reality. Discussion To our knowledge, this is the first study to use simulations to probe the causes of observed inequalities in influenza disease patterns. Knowledge of the causes and their relative explanatory power will allow us to design interventions that have the greatest impact on reducing inequalities. Conclusion Differential exposure due to population structure in our realistic simulation model explains a third of the observed inequality. Differential susceptibility to disease due to prevailing chronic conditions, vaccine uptake, and smoking should be considered in future models in order to quantify the role of additional factors in generating influenza inequalities. Electronic supplementary material The online version of this article (doi:10.1186/s12889-015-2284-2) contains supplementary material, which is available to authorized users.


Probability of Staying Home
The baseline probability that an agent stays home if the agent experiences a symptomatic infection.

Household Contact Probability
The probability of potentially infective daily contacts between an infectious agent and a susceptible agent in a household.  Epidemic Week

Relationship between poverty and demographic factors
We examined the correlation between demographic factors-population density, average household size, percent of the population below 18y of age and percent of the population above 65y of age-and the percent of the population living below the federal poverty line in the census tract. Poverty was positively correlated with population density (P < 0.001) and with the percentage of the census tract population that is below 18y age (P < 0.001). Poverty was also negatively correlated with the percentage of older adults in the census tract (P < 0.001), but uncorrelated with average household size in the census tract ( Figure S3).

Methods
To examine if factors related to population structure explained the relationship between census tract poverty and AR SIM, we included the percentage of the population in a census tract that was below the federal poverty line in all models along with its squared term to account for the curvilinear relationship between poverty and AR SIM . Population density and its squared term, average household size in a tract, the percent <18y, and the percent >=65y were each included to examine if the relationship between poverty and AR SIM was no longer significant. R 2 was examined to gauge the proportion of variance in AR SIM that was explained by any model. We deemed models to be significant based on the F-test, and model terms to be significant based on the t-test, setting p-value < 0.05 as our cutoff. Beta (standardized) coefficients for each term are reported. We examined the Akaike Information Criterion (AIC; reported in Table S3) as well as the related likelihood ratio test (not shown) to gauge parsimony.

Results
We used multiple regression to examine the demographic factors that account for the relationship between poverty and adult AR SIM in our model. Poverty in a tract explained a little more than a third of the variance in adult AR SIM (Table S3). Once population density and the percent >=65y were included in the regression equation, 46% of the variance in adult AR SIM was explained and the relation between poverty and adult AR SIM was no longer significant. This model was the most parsimonious based on the AIC. Interestingly, the percent >=65y was more important to explaining the relation between poverty and adult AR SIM than the percent <18y. We replaced percent <18y with percent of the population enrolled in school, and found similar results (not shown).

Additional Methods
We examined the weekly simulated epidemic curve for each household income-based susceptibility scenario, and note peak week, peak height, and outcomes in Table S5.
We examined possible interaction between higher neighborhood contact rates and differential susceptibility to disease by running models in which susceptibility of highest-income households was 77%, 50%, and 14% that of lowest-income households and agents had 20% higher contacts in the neighborhood compared to the calibrated value. Figure S5. Income-based difference in susceptibility impacts area-level disparities. The red dashed line represents the observed hospitalization rate ratio between the highest and lowest poverty tracts in NHC. Blue dots represent model-generated ratios as susceptibility of high-income households declined in comparison with low-income households. Orange dots represent model-generated ratios with 20% higher contacts in the neighborhood compared to the calibrated contact rate.