Estimation of age-stratified contact rates during the COVID-19 pandemic using a novel inference algorithm

How contact patterns during the COVID-19 pandemic are related to pre-pandemic contact patterns and mobility trends

BACKGROUND

Non-pharmaceutical interventions (NPIs) were adopted in Belgium in order to decrease social interactions between people and as such decrease viral transmission of SARS-CoV-2. With the aim to better evaluate the impact of NPIs on the evolution of the pandemic, an estimation of social contact patterns during the pandemic is needed when social contact patterns are not available yet in real time.

METHODS

In this paper we use a model-based approach allowing for time varying effects to evaluate whether mobility and pre-pandemic social contact patterns can be used to predict the social contact patterns observed during the COVID-19 pandemic between November 11, 2020 and July 4, 2022.

RESULTS

We found that location-specific pre-pandemic social contact patterns are good indicators for estimating social contact patterns during the pandemic. However, the relationship between both changes with time. Considering a proxy for mobility, namely the change in the number of visitors to transit stations, in interaction with pre-pandemic contacts does not explain the time-varying nature of this relationship well.

CONCLUSION

In a situation where data from social contact surveys conducted during the pandemic are not yet available, the use of a linear combination of pre-pandemic social contact patterns could prove valuable. However, translating the NPIs at a given time into appropriate coefficients remains the main challenge of such an approach. In this respect, the assumption that the time variation of the coefficients can somehow be related to aggregated mobility data seems unacceptable during our study period for estimating the number of contacts at a given time.

An analytical approach to evaluate the impact of age demographics in a pandemic

The time required to identify and confirm risk factors for new diseases and to design an appropriate treatment strategy is one of the most significant obstacles medical professionals face. Traditionally, this approach entails several clinical studies that may last several years, during which time strict preventative measures must be in place to contain the epidemic and limit the number of fatalities. Analytical tools may be used to direct and accelerate this process. This study introduces a six-state compartmental model to explain and assess the impact of age demographics by designing a dynamic, explainable analytics model of the SARS-CoV-2 coronavirus. An age-stratified mathematical model taking the form of a deterministic system of ordinary differential equations divides the population into different age groups to better understand and assess the impact of age on mortality. It also provides a more accurate and effective interpretation of the disease evolution, specifically in terms of the cumulative numbers of infected cases and deaths. The proposed Kermack-Mckendrick model is incorporated into a non-linear least-squares optimization curve-fitting problem whose optimized parameters are numerically obtained using the Levenberg-Marquard algorithm. The curve-fitting model's efficiency is proved by testing the age-stratified model's performance on three U.S. states: Connecticut, North Dakota, and South Dakota. Our results confirm that splitting the population into different age groups leads to better fitting and forecasting results overall as compared to those achieved by the traditional method, i.e., without age groups. By using comprehensive models that account for age, gender, and ethnicity, regional public health authorities may be able to avoid future epidemics from inflicting more fatalities and establish a public health policy that reduces the burden on the elderly population.

Incorporating infectious duration-dependent transmission into Bayesian epidemic models

Compartmental models are commonly used to describe the spread of infectious diseases by estimating the probabilities of transitions between important disease states. A significant challenge in fitting Bayesian compartmental models lies in the need to estimate the duration of the infectious period, based on limited data providing only symptom onset date or another proxy for the start of infectiousness. Commonly, the exponential distribution is used to describe the infectious duration, an overly simplistic approach, which is not biologically plausible. More flexible distributions can be used, but parameter identifiability and computational cost can worsen for moderately sized or large epidemics. In this article, we present a novel approach, which considers a curve of transmissibility over a fixed infectious duration. The incorporation of infectious duration-dependent (IDD) transmissibility, which decays to zero during the infectious period, is biologically reasonable for many viral infections and fixing the length of the infectious period eases computational complexity in model fitting. Through simulation, we evaluate different functional forms of IDD transmissibility curves and show that the proposed approach offers improved estimation of the time-varying reproductive number. We illustrate the benefit of our approach through a new analysis of the 1995 outbreak of Ebola Virus Disease in the Democratic Republic of the Congo.

Heterogeneity in the onwards transmission risk between local and imported cases affects practical estimates of the time-dependent reproduction number

During infectious disease outbreaks, inference of summary statistics characterizing transmission is essential for planning interventions. An important metric is the time-dependent reproduction number (Rt), which represents the expected number of secondary cases generated by each infected individual over the course of their infectious period. The value of Rt varies during an outbreak due to factors such as varying population immunity and changes to interventions, including those that affect individuals' contact networks. While it is possible to estimate a single population-wide Rt, this may belie differences in transmission between subgroups within the population. Here, we explore the effects of this heterogeneity on Rt estimates. Specifically, we consider two groups of infected hosts: those infected outside the local population (imported cases), and those infected locally (local cases). We use a Bayesian approach to estimate Rt, made available for others to use via an online tool, that accounts for differences in the onwards transmission risk from individuals in these groups. Using COVID-19 data from different regions worldwide, we show that different assumptions about the relative transmission risk between imported and local cases affect Rt estimates significantly, with implications for interventions. This highlights the need to collect data during outbreaks describing heterogeneities in transmission between different infected hosts, and to account for these heterogeneities in methods used to estimate Rt. This article is part of the theme issue 'Technical challenges of modelling real-life epidemics and examples of overcoming these'.

Technical challenges of modelling real-life epidemics and examples of overcoming these

The coronavirus disease 2019 (COVID-19) pandemic has highlighted the importance of mathematical modelling in informing and advising policy decision-making. Effective practice of mathematical modelling has challenges. These can be around the technical modelling framework and how different techniques are combined, the appropriate use of mathematical formalisms or computational languages to accurately capture the intended mechanism or process being studied, in transparency and robustness of models and numerical code, in simulating the appropriate scenarios via explicitly identifying underlying assumptions about the process in nature and simplifying approximations to facilitate modelling, in correctly quantifying the uncertainty of the model parameters and projections, in taking into account the variable quality of data sources, and applying established software engineering practices to avoid duplication of effort and ensure reproducibility of numerical results. Via a collection of 16 technical papers, this special issue aims to address some of these challenges alongside showcasing the usefulness of modelling as applied in this pandemic. This article is part of the theme issue 'Technical challenges of modelling real-life epidemics and examples of overcoming these'.

Visualization for epidemiological modelling: challenges, solutions, reflections and recommendations

We report on an ongoing collaboration between epidemiological modellers and visualization researchers by documenting and reflecting upon knowledge constructs-a series of ideas, approaches and methods taken from existing visualization research and practice-deployed and developed to support modelling of the COVID-19 pandemic. Structured independent commentary on these efforts is synthesized through iterative reflection to develop: evidence of the effectiveness and value of visualization in this context; open problems upon which the research communities may focus; guidance for future activity of this type and recommendations to safeguard the achievements and promote, advance, secure and prepare for future collaborations of this kind. In describing and comparing a series of related projects that were undertaken in unprecedented conditions, our hope is that this unique report, and its rich interactive supplementary materials, will guide the scientific community in embracing visualization in its observation, analysis and modelling of data as well as in disseminating findings. Equally we hope to encourage the visualization community to engage with impactful science in addressing its emerging data challenges. If we are successful, this showcase of activity may stimulate mutually beneficial engagement between communities with complementary expertise to address problems of significance in epidemiology and beyond. See https://ramp-vis.github.io/RAMPVIS-PhilTransA-Supplement/. This article is part of the theme issue 'Technical challenges of modelling real-life epidemics and examples of overcoming these'.

An algebraic framework for structured epidemic modelling

Pandemic management requires that scientists rapidly formulate and analyse epidemiological models in order to forecast the spread of disease and the effects of mitigation strategies. Scientists must modify existing models and create novel ones in light of new biological data and policy changes such as social distancing and vaccination. Traditional scientific modelling workflows detach the structure of a model-its submodels and their interactions-from its implementation in software. Consequently, incorporating local changes to model components may require global edits to the code base through a manual, time-intensive and error-prone process. We propose a compositional modelling framework that uses high-level algebraic structures to capture domain-specific scientific knowledge and bridge the gap between how scientists think about models and the code that implements them. These algebraic structures, grounded in applied category theory, simplify and expedite modelling tasks such as model specification, stratification, analysis and calibration. With their structure made explicit, models also become easier to communicate, criticize and refine in light of stakeholder feedback. This article is part of the theme issue 'Technical challenges of modelling real-life epidemics and examples of overcoming these'.

Visualization for epidemiological modelling: challenges, solutions, reflections and recommendations

We report on an ongoing collaboration between epidemiological modellers and visualization researchers by documenting and reflecting upon knowledge constructs-a series of ideas, approaches and methods taken from existing visualization research and practice-deployed and developed to support modelling of the COVID-19 pandemic. Structured independent commentary on these efforts is synthesized through iterative reflection to develop: evidence of the effectiveness and value of visualization in this context; open problems upon which the research communities may focus; guidance for future activity of this type and recommendations to safeguard the achievements and promote, advance, secure and prepare for future collaborations of this kind. In describing and comparing a series of related projects that were undertaken in unprecedented conditions, our hope is that this unique report, and its rich interactive supplementary materials, will guide the scientific community in embracing visualization in its observation, analysis and modelling of data as well as in disseminating findings. Equally we hope to encourage the visualization community to engage with impactful science in addressing its emerging data challenges. If we are successful, this showcase of activity may stimulate mutually beneficial engagement between communities with complementary expertise to address problems of significance in epidemiology and beyond. See https://ramp-vis.github.io/RAMPVIS-PhilTransA-Supplement/. This article is part of the theme issue 'Technical challenges of modelling real-life epidemics and examples of overcoming these'.

Modelling: Understanding pandemics and how to control them

New disease challenges, societal demands and better or novel types of data, drive innovations in the structure, formulation and analysis of epidemic models. Innovations in modelling can lead to new insights into epidemic processes and better use of available data, yielding improved disease control and stimulating collection of better data and new data types. Here we identify key challenges for the structure, formulation, analysis and use of mathematical models of pathogen transmission relevant to current and future pandemics.