Multivariable Behavioral Change Modeling of Epidemics in the Presence of Undetected Infections

TL;DR

This work develops a fully Bayesian, stochastic epidemic framework that links transmission dynamics to population behavior through a multivariable alarm driven by observed cases and deaths. By extending to an SIHRD structure with undetected infections and employing data augmentation, the authors jointly infer transmission, disease progression, and behaviors while quantifying uncertainty. Through simulations and real-data analyses of two COVID-19 waves in Miami and Montréal, the approach demonstrates improved fit and interpretable insight into how cases and deaths shape behavior and, consequently, the time-varying reproductive number $\mathcal{R}_0(t)$. The study highlights the value of integrating multiple data streams, addressing under-detection, and explicitly modeling behavioral responses to inform public health policy and resource planning.

Abstract

Epidemic models are invaluable tools to understand and implement strategies to control the spread of infectious diseases, as well as to inform public health policies and resource allocation. However, current modeling approaches have limitations that reduce their practical utility, such as the exclusion of human behavioral change in response to the epidemic or ignoring the presence of undetected infectious individuals in the population. These limitations became particularly evident during the COVID-19 pandemic, underscoring the need for more accurate and informative models. To address these challenges, we develop a novel Bayesian epidemic modeling framework to better capture the complexities of disease spread by incorporating behavioral responses and undetected infections. In particular, our framework makes three contributions: 1) leveraging additional data on hospitalizations and deaths in modeling the disease dynamics, 2) accounting for data uncertainty arising from the large presence of asymptomatic and undetected infections, and 3) allowing the population behavioral change to be dynamically influenced by multiple data sources (cases and deaths). We thoroughly investigate the properties of the proposed model via simulation, and illustrate its utility on COVID-19 data from Montreal and Miami.

Figures (7)

• Figure 1: Simulated epidemics from three scenarios capturing various importance of cases and deaths informing behavioral change. Plotted over time are the total (unobserved) infections (dashed gray), observed cases (solid black), hospitalizations (solid gold), and deaths (solid blue). In the high deaths importance scenario, infections peak at counts around 3,000 but this was excluded from the figure to highlight more subtle differences between high case importance and equal importance generating scenarios.
• Figure 2: Root mean squared error (RMSE) of the effective reproductive number, $\mathcal{R}_0(t)$, at the start and end of the simulated epidemics for the three data generating scenarios, the SIHRD and SIR models, and modeling or ignoring undetected infections.
• Figure 3: Posterior predictive means (dashed lines) and 95% credible intervals (shaded regions) for one randomly selected simulation compared to true cases (solid black), hospitalizations (solid gold), and deaths (solid blue).
• Figure 4: Posterior means and 95% credible intervals for $\alpha$ across all simulations for the three data generating scenarios (columns) and the SIHRD and SIR models with multivariable behavioral change as specified in Equation \ref{['eq_multialarm']} (rows). The true parameters used in simulation are shown by the dashed red lines.
• Figure 5: COVID-19 case and death rates per 100,000 during 2020 in Miami-Dade County, Florida and Montréal, Québec. Gray shaded regions are those used in model fitting. In Miami, Wave 1 started on March 11, 2020 and Wave 2 started on June 1. In Montréal, Wave 1 started on March 5, 2020 and Wave 2 started on August 23, 2020.