Modeling the joint socio-structural and spatial drivers of infection inequity

Statistical Methods for Infectious Disease Across Scales

Penn State University

2024-04-05

Jon Zelner

Dept. of Epidemiology

Center for Social Epidemiology and Population Health

University of Michigan School of Public Health

✉️ `jzelner@umich.edu`

🌐 `epibayes.io`

Brief overview of what has - and hasn’t - been done to mechanistically link residential segregation to infection inequity.

An attempt to make sense of the impact of different aspects of segregation on basic quantities like \(R_0\).

Discussion of what this all has to do with spatial analysis.

Segregation restricts access to healthcare and health-promoting physical environments.

Inequity in purchasing power due to artificially inflated housing, food and other costs.

Increased risk of crime victimization, overpolicing, and police violence.

How to apply this thinking to infectious disease transmission is still very much an open question.

Spatial separation is the most obvious feature of segregation.

Often captured by metrics of clustering or spatial distributiuon including dissimilarity and Moran’s I.

When we conflate separation with vulnerability, we risk attributing the wrong spatial causes to disparities in infection outcomes.

- Dissimilarity measures the proportion of members of the
*minority*group who would have to move to achieve proportional mixing.

- Commonly used to measure spatial segregation in demographic and disease data.

- Measure is independent of density.

- Random mixing occurs in the situation dissimilarity = 0, no mixing when dissimilarity = 1

Represents the relative increase in per-contact risk of infection among members of segregated populations.

Can also be thought of as relative vulnerability to infection.

May result from household crowding, increased occupational risk, comorbidities and other factors

\(\epsilon\) controls spatial dissimilarity, i.e. the degree of within vs. between-group mixing.

Parameter \(\rho \ge 1\) characterizes the change in risk associated with increasing concentration.

Use the spectral approach to estimating \(R_0\) (10) and numerical simulation to understand the implications of these mechanisms.

\[ \begin{aligned} \lambda_1 &= \beta \rho S_1 \left(\epsilon \frac{ I_1}{N_1} + (1-\epsilon)\frac{I_1 + I_2}{N}\right) \\ \lambda_2 &= \beta S_2 \left(\epsilon \frac{I_2}{N_2} + (1-\epsilon)\frac{I_1 + I_2}{N}\right) \\ \end{aligned} \qquad(1)\]

Representative of an endemic infection with no protection against reinfection.

Useful for looking at broad patterns of inequity.

Pathogen-specific natural histories will be necessary for thinking more concretely about interventions etc.

\[ \begin{aligned} \frac{dS_1}{dt} &= - \lambda_1 + \gamma I_1 \\ \frac{dS_2}{dt} &= -\lambda_2 + \gamma I_2 \\ \frac{dI_1}{dt} &= \lambda_1 - \gamma I_1 \\ \frac{dI_2}{dt} &= \lambda_2 - \gamma I_2 \end{aligned} \]

We should expect the observable dimensions of segregation to be *correlated* since they share a common, fundamental, cause.

**We can model \(\rho\) as a function of \(\epsilon\)**

\[ \rho(\epsilon) = 1 + (1- \epsilon) \zeta_\rho \]

Where \(\zeta_\rho\) is the maximum vulnerability when \(\epsilon = 1\)

Mismatch between individual-level outcomes and spatialized measures (i.e. ecological fallacy).

Increasing reliance on non-mechanistic metrics of social risks, e.g. social vulnerabulity index.

Non-random missingness of key demographic covariates (e.g. race & ethnicity).

Flaky population denominators that get worse as you break them down more.

We haven’t touched on differential outcomes of infection including death and severe disease.

How do we go from this very simple framework to real-world data?

What implications are there for prevention and intervention?

Work supported by NIMHD R01MD017218

For more info abour our research check out epibayes.io

Related tutorials and teaching materials on my blog at zelnotes.io

I have to leave midday tomorrow to hopefully not injure myself at my daughter’s 7th birthday party at a trampoline park.

So: Please send me a note at

`jzelner@umich.edu`

if any of this is of interest and we don’t get to talk!

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