PDE

📈 The Hybrid ODE–PDE Epidemic Transport Model: Quantifying Spatiotemporal Spread 🌍

by

🧬 Overview and Conceptual Motivation In many real-world epidemics, the assumption of a perfectly well-mixed population fails to capture observed patterns of spread. The Hybrid ODE–PDE Epidemic Transport Model addresses this limitation by explicitly coupling local biological dynamics with spatial movement. Ordinary Differential Equations (ODEs) describe infection processes at a specific location, while Partial Differential … Read more

🌊 The Epidemic Wave: Mapping Spatial Spread through Reaction–Diffusion Dynamics

by

🧬 Overview and Conceptual Motivation Standard compartmental epidemic models describe how infections evolve over time but typically ignore spatial structure, effectively treating the population as a single point in space. The Epidemic Wave, or Traveling Wave Reaction–Diffusion Model, extends these approaches by explicitly incorporating geographical movement. By coupling local transmission processes with spatial diffusion, the … Read more

🧬 Antigenic Drift Diffusion: Modeling the Evolution of Viral Escape

by

📈 Conceptual Overview For rapidly evolving viruses such as Influenza and SARS-CoV-2, classical compartmental models assuming a static pathogen are insufficient. The Antigenic Drift Diffusion model extends epidemic modeling by treating viral antigenic properties as a continuous trait, allowing explicit representation of immune escape through gradual mutation. In this framework, viral strains move through an … Read more

📊 The Age-of-Infection Model: Precision in Epidemic Modeling

by

📈 Overview and Conceptual Motivation In classical epidemiology, it is often assumed that all infected individuals are equally infectious throughout their infectious period. The Age-of-Infection (also called Infection-Age) Model relaxes this assumption by explicitly recognizing that both infectiousness and removal depend on the time elapsed since infection. This framework is essential for diseases in which … Read more

🔬 Synergistic Spatial Modeling: Coupling PDEs and ABMs for Viral Dynamics

by

🧭 Overview Hybrid epidemiological models represent a major methodological advancement by explicitly coupling Agent-Based Models (ABMs) with Partial Differential Equation (PDE) frameworks. This approach addresses a central limitation in large-scale epidemic modeling: ABMs provide realistic, individual-level resolution but become computationally prohibitive at scale, while PDEs efficiently describe continuous spatial spread but lack behavioral granularity. Hybrid … Read more

🔬 Stochastic Efficiency: The Compartment–Agent Mixed Model (CAMM)

by

🧭 Overview The Compartment–Agent Mixed Model (CAMM) is a stochastic epidemiological modeling framework designed to overcome the computational limitations of large-scale Agent-Based Models while preserving essential stochastic behavior. CAMM provides a hybrid paradigm that combines the mathematical clarity and efficiency of classical compartmental models with the flexibility of agent-based simulation. Instead of modeling every individual … Read more

🐼 Pandaesim: Stochastic Simulation for Age-Structured Epidemic Dynamics

by

🧭 Overview Pandaesim is an epidemic spreading simulator designed to analyze complex infectious disease dynamics using stochastic or deterministic age-structured compartmental models embedded within a meta-population framework. It was developed to study large-scale epidemics such as COVID-19, where age-specific susceptibility, contact behavior, and spatial movement strongly influence transmission patterns. By combining age stratification with an … Read more

💧 Hydrology Meets Epidemiology: The HYDREMATS Vector Model

by

🧭 Overview The HYDREMATS (Hydrology, Entomology, and Malaria Transmission Simulation) model is a spatially explicit Agent-Based Model designed to simulate malaria vector dynamics, particularly for Anopheles mosquito species, at the village scale. Its defining characteristic is the tight yet modular coupling of a distributed hydrology model with a mosquito agent-based model, allowing environmental physics to … Read more

🛣️ Trajectory Networks in Epidemiology: Tracking Epidemic Spread through Human Mobility

by

Trajectory Network modeling is an advanced approach at the intersection of spatial epidemiology, network science, and human mobility analysis. It focuses on epidemic spreading driven by explicit individual movement paths—such as pedestrian trajectories, commuting routes, or vehicular flows—rather than assuming static contacts or homogeneous mixing. By transforming raw trajectory data into dynamic networks, this framework … Read more

🌐 Networked Dynamics: Spatial Metapopulation Models for Epidemic Forecasting

by

Spatial Network Models, most commonly implemented through the Metapopulation framework, are core tools in mathematical epidemiology for forecasting infectious disease spread across geographically distinct populations. These models explicitly link local disease dynamics within each population unit to mobility-driven interactions between units, enabling rigorous analysis of how human movement shapes the large-scale diffusion, synchronization, and timing … Read more