Paper List
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Pharmacophore-based design by learning on voxel grids
This paper addresses the computational bottleneck and limited novelty in conventional pharmacophore-based virtual screening by introducing a voxel cap...
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CONFIDE: Hallucination Assessment for Reliable Biomolecular Structure Prediction and Design
This paper addresses the critical limitation of current protein structure prediction models (like AlphaFold3) where high-confidence scores (pLDDT) can...
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On the Approximation of Phylogenetic Distance Functions by Artificial Neural Networks
This paper addresses the core challenge of developing computationally efficient and scalable neural network architectures that can learn accurate phyl...
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EcoCast: A Spatio-Temporal Model for Continual Biodiversity and Climate Risk Forecasting
This paper addresses the critical bottleneck in conservation: the lack of timely, high-resolution, near-term forecasts of species distribution shifts ...
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Training Dynamics of Learning 3D-Rotational Equivariance
This work addresses the core dilemma of whether to use computationally expensive equivariant architectures or faster symmetry-agnostic models with dat...
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Fast and Accurate Node-Age Estimation Under Fossil Calibration Uncertainty Using the Adjusted Pairwise Likelihood
This paper addresses the dual challenge of computational inefficiency and sensitivity to fossil calibration errors in Bayesian divergence time estimat...
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Few-shot Protein Fitness Prediction via In-context Learning and Test-time Training
This paper addresses the core challenge of accurately predicting protein fitness with only a handful of experimental observations, where data collecti...
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scCluBench: Comprehensive Benchmarking of Clustering Algorithms for Single-Cell RNA Sequencing
This paper addresses the critical gap of fragmented and non-standardized benchmarking in single-cell RNA-seq clustering, which hinders objective compa...
The Effective Reproduction Number in the Kermack-McKendrick model with age of infection and reinfection
School of Mathematical Sciences, Beijing Normal University, Beijing 100875, People’s Republic of China.
The 30-Second View
IN SHORT: This paper addresses the challenge of accurately estimating the time-varying effective reproduction number ℛ(t) in epidemics by incorporating two critical real-world complexities: the age of infection (time since infection) and the possibility of reinfection.
Innovation (TL;DR)
- Methodology Introduces a novel extension of the classical Kermack-McKendrick SIRS model by formally incorporating both infection-age structure (a) and a reinfection term (δ), moving beyond constant transmission rate assumptions.
- Methodology Derives a rigorous mathematical framework using Volterra integral equations, the contraction mapping principle, and measure-valued solutions (e.g., Dirac mass for initial cohorts) to connect the flow of new infections N(t) to the reproductive power ℛ(t,a) and ultimately ℛ(t).
- Methodology/Biology Develops a practical parameter identification methodology that works with two common but challenging data types: 1) direct daily new case counts (applied to 2003 SARS in Singapore) and 2) cumulative death counts when new infection data is unreliable (applied to COVID-19 in China).
Key conclusions
- The model successfully formulates the infection dynamics as a nonlinear Volterra integral equation of the second kind for N(t) (Eq. 2.14), providing a solvable link between observable data and the underlying transmission parameters.
- Theoretical analysis justifies the use of a Dirac mass initial condition (representing a single cohort infected at time t0) via a limiting process of approximating functions i_κ(a), proving uniform convergence of the solution N_κ(t) to N(t) (Theorem 3.2).
- The derived framework enables the identification of the effective reproduction number ℛ(t) from epidemic curves, demonstrated through application to real-world SARS and COVID-19 datasets, bridging theoretical constructs with practical public health analytics.
Abstract: This study introduces a novel epidemiological model that expands upon the Kermack-McKendrick model by incorporating the age of infection and reinfection. By including infection age, we can classify participants, which enables a more targeted analysis within the modeling framework. The reinfection term addresses the real-world occurrences of secondary or recurrent viral infections. In the theoretical part, we apply the contraction mapping principle, the dominated convergence theorem, and the properties of Volterra integral equations to derive analytical expressions for the number of newly infected individuals denoted by N(t). Then, we establish a Volterra integral equation for N(t) and study its initial conditions for both a single cohort and multiple cohorts. From this equation, we derive a method for identifying the effective reproduction number, denoted as ℛ(t). In the practical aspect, we present two distinct methods and separately apply them to analyze the daily new infection cases from the 2003 SARS outbreak in Singapore and the cumulative number of deaths from the COVID-19 epidemic in China. This work effectively bridges theoretical epidemiology and computational modeling, providing a robust framework for analyzing infection dynamics influenced by infection-age-structured transmission and reinfection mechanisms.