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

Abstract

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.

Highlights: 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.

Keywords: COVID-19; correctional facility; infectious diseases; meta-model.

Figure 1/. Model schematic.

We developed a stochastic model of infections within and between a correctional facility and community using the tau-leap method. We considered three populations: (1) inmates, (2) correctional staff, and (3) community members. For these populations, we tracked health states including susceptible (S), infected (I), detected (D), and recovered (R). Epidemiological parameters governed disease progression shown by the solid arrows. Movement parameters governed movements between populations, shown by the dashed arrows, including the incarcerations and release rate (e) and the fraction of time staff spend in the correctional facility (f) versus in the community.

Figure 2/. Existence of a magnification-reflection dynamic in a specific setting.

For our base case analysis of COVID-19 caused by the SARS-CoV-2 wild-type strain in a prison and community the size of a typical zip code, we projected the expected per capita infection prevalence over time with and without connection between the prison and community. With connection, infections can be transmitted between the populations. Time refers to the days following the first infection in the community. This dynamic also exists for other diseases and settings (Supplement S1).

Figure 3/. Drivers of the magnification-reflection dynamic.

For our base case analysis of COVID-19 caused by the SARS-CoV-2 wild-type strain in a prison and community the size of a typical zip code, we varied parameters one at a time to reflect diversity in prisons and communities. We projected the difference in expected infection prevalence (per 100k people) over time with and without connection between the prison and community. Shown here are three key drivers. These drivers were consistent for other diseases and settings (Supplement S2).

Figure 4/. Relative importance of infection routes.

For various diseases and settings, we projected the percent reduction in expected infections with no resident movement (i.e., no incarcerations and releases), no staff movement, and neither movement. The error bars show 90% credible intervals. Abbreviations: COVID-19 WT, COVID-19 caused by the SARS-CoV-2 wild-type strain; COVID-19 Delta, COVID-19 caused by the SARS-CoV-2 Delta variant.

Figure 5/. Partial dependence plots.

We trained machine learning models to predict the difference in expected infections (per 100k people) with and without connection between the correctional facility and community for prisons and jails, respectively. We generated partial dependence plots, which show the marginal effect of each variable on the mean response (i.e., mean model outcome, which is in units of infections per 100k people). Shown here are results for the three key variables from Figure 3 in addition to staff population and incarceration and release rate. See Supplement S4A for partial dependence plots for all variables. Abbreviations: COVID-19 WT, COVID-19 caused by the SARS-CoV-2 wild-type strain; COVID-19 Delta, COVID-19 caused by the SARS-CoV-2 Delta variant.