Dynamics of Respiratory Infectious Diseases in Incarcerated and Free-Living Populations: A Simulation Modeling Study

Background: Historically, correctional facilities have had large outbreaks of respiratory infectious diseases like COVID-19. Hence, importation and exportation of such diseases from correctional facilities raises substantial concern. Methods: We developed a stochastic simulation model of transmission of respiratory infectious diseases within and between correctional facilities and the community. We investigated the infection dynamics, key governing factors, and relative importance of different infection routes (e.g., incarcerations and releases versus correctional staff). We also developed machine-learning meta-models of the simulation model, which allowed us to examine how our findings depended on different disease, correctional facility, and community characteristics. Results: We find a magnification-reflection dynamic: a small outbreak in the community can cause a larger outbreak in the correction facility, which can then cause a second, larger outbreak in the community. This dynamic is strongest when community size is relatively small as compared with the size of the correctional population, the initial community R-effective is near 1, and initial prevalence of immunity in the correctional population is low. The timing of the correctional magnification and community reflection peaks in infection prevalence are primarily governed by the initial R-effective for each setting. Because the release rates from prisons are low, our model suggests correctional staff may be a more important infection entry route into prisons than incarcerations and releases; in jails, where incarceration and release rates are much higher, our model suggests the opposite. Conclusions: We find that across many combinations of respiratory pathogens, correctional settings, and communities, there can be substantial magnification-reflection dynamics, which are governed by several key factors. Our goal was to derive theoretical insights relevant to many contexts; our findings should be interpreted accordingly. We find a magnification-reflection dynamic: a small outbreak in a community can cause a larger outbreak in a correctional facility, which can then cause a second, larger outbreak in the community. For public health decision makers considering contexts most susceptible to this dynamic, we find that the dynamic is strongest when the community size is relatively small, initial community R-effective is near 1, and the initial prevalence of immunity in the correctional population is low; the timing of the correctional magnification and community reflection peaks in infection prevalence are primarily governed by the initial R-effective for each setting. We find that correctional staff may be a more important infection entry route into prisons than incarcerations and releases; however, for jails, the relative importance of the entry routes may be reversed. For modelers, we combine simulation modeling, machine-learning meta-modeling, and interpretable machine learning to examine how our findings depend on different disease, correctional facility, and community characteristics; we find they are generally robust.