A Unified Multi-State Approach for Investigating the Dynamics of Chronic and Infectious Diseases

Infectious diseases and chronic diseases are two major fields in epidemiology that have traditionally been studied separately because of their distinct etiologies and modeling methods. Infectious disease data are typically collected at an aggregated level and analyzed using compartmental models, most commonly the susceptible (S), infectious (I), and recovered (R) (SIR) model, whereas chronic disease data are usually collected at the individual level and analyzed using multi-state survival models. Previous studies have pointed out the link between compartmental models and survival analysis by reconstructing the aggregated infection disease data into individual-level data. However, these studies have largely focused on the two-state transition from S to I state, and few studies have simultaneously modeled the three-state process, S, I, and R. In this paper, we propose to use a discrete-time multi-state framework to model the three-state progression of infectious disease. We first introduce and compare the underlying methodological foundations for modeling infectious disease and chronic disease dynamics, then show the link between compartment models and multi-state models, and finally present how infectious disease can be modeled using the multi-state framework under the two scenarios: 1) all S, I, and R states are observed, and 2) only the I state is observed, with the R state treated as latent. In the application, we applied the multi-state approach to estimate the dynamics of influenza using the data in a British boarding school in 1978, where only the infected cases were observed over time. The estimated recovery rate was 0.42 and the corresponding contact rate was0.91 (95% CI: 0.84, 0.98). The basic reproductive number was 2.17 (95% CI: 2.00, 2.33), which declined to approximately 1 by day 6, and continued to decrease thereafter. Overall, we propose a unified multi-state approach for modeling infectious and chronic disease progression, which may provide evidence to inform timely and effective infectious disease prevention.