Structural causal influence (SCI) captures the forces of social inequality in models of disease dynamics

Mathematical modelling has served a central role in studying how infectious disease transmission manifests at the population level. These models have demonstrated the importance of population-level factors like social network heterogeneity on structuring epidemic risk and are now routinely used in public health for decision support. One barrier to broader utility of mathematical models is that the existing canon does not readily accommodate the social determinants of health as distinct, formal drivers of transmission dynamics. Given the decades of empirical support for the organizational effect of social determinants on health burden more generally and infectious disease risk more specially, addressing this modelling gap is of critical importance. In this study, we build on prior efforts to integrate social forces into mathematical epidemiology by introducing several new metrics, principally structural causal influence (SCI). Here, SCI leverages causal analysis to provide a measure of the relative vulnerability of subgroups within a susceptible population, which are crafted by differences in healthcare, exposure to disease, and other determinants. We develop our metrics using a general case and apply it to specific one of public health importance: Hepatitis C virus in a population of persons who inject drugs. Our use of the SCI reveals that, under specific parameters in a multi-community model, the "less vulnerable" community may sustain a basic reproduction number below one when isolated, ensuring disease extinction. However, even minimal transmission between less and more vulnerable communities can elevate this number, leading to sustained epidemics within both communities. Summarizing, we reflect on our findings in light of conversations surrounding the importance of social inequalities and how their consideration can influence the study and practice of mathematical epidemiology.