Inferring the effective reproductive number from deterministic and semi-deterministic compartmental models using incidence and mobility data

A flexible framework for local-level estimation of the effective reproductive number in geographic regions with sparse data

BACKGROUND

Our research focuses on local-level estimation of the effective reproductive number, which describes the transmissibility of an infectious disease and represents the average number of individuals one infectious person infects at a given time. The ability to accurately estimate the infectious disease reproductive number in geographically granular regions is critical for disaster planning and resource allocation. However, not all regions have sufficient infectious disease outcome data; this lack of data presents a significant challenge for accurate estimation.

METHODS

To overcome this challenge, we propose a two-step approach that incorporates existing [Formula: see text] estimation procedures (EpiEstim, EpiFilter, EpiNow2) using data from geographic regions with sufficient data (step 1), into a covariate-adjusted Bayesian Integrated Nested Laplace Approximation (INLA) spatial model to predict [Formula: see text] in regions with sparse or missing data (step 2). Our flexible framework effectively allows us to implement any existing estimation procedure for [Formula: see text] in regions with coarse or entirely missing data. We perform external validation and a simulation study to evaluate the proposed method and assess its predictive performance.

RESULTS

We applied our method to estimate [Formula: see text]using data from South Carolina (SC) counties and ZIP codes during the first COVID-19 wave ('Wave 1', June 16, 2020 - August 31, 2020) and the second wave ('Wave 2', December 16, 2020 - March 02, 2021). Among the three methods used in the first step, EpiNow2 yielded the highest accuracy of [Formula: see text] prediction in the regions with entirely missing data. Median county-level percentage agreement (PA) was 90.9% (Interquartile Range, IQR: 89.9-92.0%) and 92.5% (IQR: 91.6-93.4%) for Wave 1 and 2, respectively. Median zip code-level PA was 95.2% (IQR: 94.4-95.7%) and 96.5% (IQR: 95.8-97.1%) for Wave 1 and 2, respectively. Using EpiEstim, EpiFilter, and an ensemble-based approach yielded median PA ranging from 81.9 to 90.0%, 87.2-92.1%, and 88.4-90.9%, respectively, across both waves and geographic granularities.

CONCLUSION

These findings demonstrate that the proposed methodology is a useful tool for small-area estimation of [Formula: see text], as our flexible framework yields high prediction accuracy for regions with coarse or missing data.

A Flexible Framework for Local-Level Estimation of the Effective Reproductive Number in Geographic Regions with Sparse Data

Background

Our research focuses on local-level estimation of the effective reproductive number, which describes the transmissibility of an infectious disease and represents the average number of individuals one infectious person infects at a given time. The ability to accurately estimate the infectious disease reproductive number in geographically granular regions is critical for disaster planning and resource allocation. However, not all regions have sufficient infectious disease outcome data; this lack of data presents a significant challenge for accurate estimation.

Methods

To overcome this challenge, we propose a two-step approach that incorporates existingR t estimation procedures (EpiEstim, EpiFilter, EpiNow2) using data from geographic regions with sufficient data (step 1), into a covariate-adjusted Bayesian Integrated Nested Laplace Approximation (INLA) spatial model to predictR t in regions with sparse or missing data (step 2). Our flexible framework effectively allows us to implement any existing estimation procedure forR t in regions with coarse or entirely missing data. We perform external validation and a simulation study to evaluate the proposed method and assess its predictive performance.

Results

We applied our method to estimateR t using data from South Carolina (SC) counties and ZIP codes during the first COVID-19 wave ('Wave 1', June 16, 2020 - August 31, 2020) and the second wave ('Wave 2', December 16, 2020 - March 02, 2021). Among the three methods used in the first step, EpiNow2 yielded the highest accuracy ofR t prediction in the regions with entirely missing data. Median county-level percentage agreement (PA) was 90.9% (Interquartile Range, IQR: 89.9-92.0%) and 92.5% (IQR: 91.6-93.4%) for Wave 1 and 2, respectively. Median zip code-level PA was 95.2% (IQR: 94.4-95.7%) and 96.5% (IQR: 95.8-97.1%) for Wave 1 and 2, respectively. Using EpiEstim, EpiFilter, and an ensemble-based approach yielded median PA ranging from 81.9%-90.0%, 87.2%-92.1%, and 88.4%-90.9%, respectively, across both waves and geographic granularities.

Conclusion

These findings demonstrate that the proposed methodology is a useful tool for small-area estimation ofR t , as our flexible framework yields high prediction accuracy for regions with coarse or missing data.

Biosafety Issues in Patient Transport during COVID-19: A Case Study on the Portuguese Emergency Services

During the COVID-19 pandemic, first responders faced significant biosafety challenges, especially while handling patient transport, potentially exposing them to infection. The PANDEM-2 (European project on pandemic preparedness and response) project, funded by the Horizon 2020 program, sought to investigate the challenges confronting Emergency Medical Systems throughout the EU. First responders from Portugal's National Institute of Medical Emergency (INEM) were considered as a representative operational model of the national first responder agencies of European member states because they played a critical role during the COVID-19 pandemic. As a result, they were asked to complete an online survey about their COVID-19 pandemic-related professional activities. The survey focused on their perspectives on current biosafety guidelines and their operational practices. It covered opinions on existing protocols, technical concerns during patient transport, and issues after the patients arrived at the hospital. The key findings revealed concerns about risk assessment, the inadequacy of guidelines, and disparities in equipment access. This survey emphasizes the importance of developing streamlined, adaptable biosafety protocols, better coordination between prehospital and in-hospital services, and the development of scalable, cost-effective biosafety solutions. Based on our findings, we propose improvements to national and European biosafety directives and advocate for streamlined adaptation during pandemics.

Mathematical modeling of the infectious spread and outbreak dynamics of avian influenza with seasonality transmission for chicken farms

A compartmental model with a time-varying contact rate, the seasonality effect, and its corresponding nonautonomous model are investigated. The model is developed based on the six compartments: susceptible, latent, infected, asymptomatic, treated, and recovered individuals. We determine the effective reproduction number for this nonautonomous system, and analytic discussion shows that at least one positive periodic solution exists for R0>1. The model is simulated using the RK-45 numerical method, and the parameter values for the model are taken from the available literature. From the numerical results, we observe that the degree of seasonality and vaccine efficacy significantly impact the amplitude of the epidemic curve. The latent-infected phase plane shows that periodic solutions exhibit a period-doubling bifurcation as the amplitude of seasonality increases. Finally, the model outcome was compared with the actual field data and found to be consistent.

An immuno-epidemiological model for transient immune protection: A case study for viral respiratory infections

The dynamics of infectious disease in a population critically involves both within-host pathogen replication and between host pathogen transmission. While modeling efforts have recently explored how within-host dynamics contribute to shaping population transmission, fewer have explored how ongoing circulation of an epidemic infectious disease can impact within-host immunological dynamics. We present a simple, influenza-inspired model that explores the potential for re-exposure during a single, ongoing outbreak to shape individual immune response and epidemiological potential in non-trivial ways. We show how even a simplified system can exhibit complex ongoing dynamics and sensitive thresholds in behavior. We also find epidemiological stochasticity likely plays a critical role in reinfection or in the maintenance of individual immunological protection over time.

Anchoring the mean generation time in the SEIR to mitigate biases in ℜ0 estimates due to uncertainty in the distribution of the epidemiological delays

The basic reproduction number, ℜ 0 , is of paramount importance in the study of infectious disease dynamics. Primarily, ℜ 0 serves as an indicator of the transmission potential of an emerging infectious disease and the effort required to control the invading pathogen. However, its estimates from compartmental models are strongly conditioned by assumptions in the model structure, such as the distributions of the latent and infectious periods (epidemiological delays). To further complicate matters, models with dissimilar delay structures produce equivalent incidence dynamics. Following a simulation study, we reveal that the nature of such equivalency stems from a linear relationship between ℜ 0 and the mean generation time, along with adjustments to other parameters in the model. Leveraging this knowledge, we propose and successfully test an alternative parametrization of the SEIR model that produces accurate ℜ 0 estimates regardless of the distribution of the epidemiological delays, at the expense of biases in other quantities deemed of lesser importance. We further explore this approach's robustness by testing various transmissibility levels, generation times and data fidelity (overdispersion). Finally, we apply the proposed approach to data from the 1918 influenza pandemic. We anticipate that this work will mitigate biases in estimating ℜ 0 .