Ziwang Deng

🧠 The Neural SIR Model: Mechanistic Modeling Meets Deep Learning

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The Neural SIR Model represents a major methodological advance in mathematical epidemiology by integrating the classical mechanistic Susceptible–Infectious–Recovered (SIR) framework with modern deep learning techniques, particularly Physics-Informed Neural Networks. This hybrid paradigm preserves the interpretability and biological grounding of differential equation–based models while exploiting the expressive power of neural networks for accurate parameter inference and … Read more

📈 Unlocking Spatial Dynamics: The Kernel-Modulated SIR Model

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The Kernel-Modulated Susceptible–Infectious–Recovered (SIR) model is a mechanistic framework widely used in mathematical epidemiology to simulate contagious disease spread across large geographical scales, ranging from counties to entire continents. The model extends the classical SIR structure by embedding spatial interaction and movement dynamics directly into the transmission process through a modulating kernel. This kernel captures … Read more

📉⛈️ Stochastic Differential Equation (SDE) Models: Modeling Noise in Epidemic Trajectories

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Stochastic Differential Equation (SDE) models constitute a powerful class of stochastic compartmental models that extend deterministic epidemic frameworks by explicitly incorporating continuous random perturbations. Rather than assuming fixed transmission and recovery rates, SDEs recognize that epidemiological processes are influenced by ongoing environmental variability, demographic fluctuations, and unobserved behavioral changes. By embedding noise terms directly into … Read more

⏳🎲 Discrete Time Markov Chain (DTMC) Models: Quantifying Epidemic Risk in Generations

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Discrete Time Markov Chain (DTMC) models are a foundational class of stochastic compartmental models in mathematical epidemiology. They are designed to represent epidemic dynamics over fixed, discrete time intervals, such as days or entire generations of infection. Unlike deterministic ordinary differential equation models, DTMCs explicitly incorporate randomness through probability laws, making them particularly suitable for … Read more

🎲📈 Continuous Time Markov Chain (CTMC) Models: Incorporating Stochasticity into Compartmental Epidemiology

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Continuous Time Markov Chain (CTMC) models form a foundational class of stochastic compartmental models in mathematical epidemiology. In contrast to deterministic ordinary differential equation (ODE) models, which describe average behavior in large populations, CTMC models explicitly incorporate randomness through probabilistic transition mechanisms. This allows them to capture demographic stochasticity, chance extinction, and variability in outbreak … Read more

✈️🏙️ Bidirectional Mobility Agent-Based Models: Modeling Spread Through Dynamic Location Exchange

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The Bidirectional Mobility Model, when implemented as an Agent-Based Model (ABM), is designed to capture the dynamic spatial spread of infectious diseases driven by the movement of individuals between discrete, geographically distinct locations, such as neighborhoods, cities, or regions. In this framework, the population is represented as a collection of agents, each possessing both a … Read more

📶🔗 Multilayer Network Agent-Based Models: Modeling Multiple Contact Structures Simultaneously

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Multilayer Network Agent-Based Models (ABMs) represent a major advance in epidemiological modeling by explicitly recognizing that individuals simultaneously participate in multiple, distinct contact environments, such as households, workplaces, schools, and the broader community. In this framework, the population is modeled as a single set of agents, while interactions are represented through several superimposed network layers, … Read more

📊 Configuration Model Agent-Based Models: Prescribing Epidemic Dynamics via Degree Distribution

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The Configuration Model (CM) occupies a central position among network-based Agent-Based Models (ABMs) by explicitly encoding observed social heterogeneity into the model structure. Unlike purely random network constructions, the Configuration Model allows the modeler to prescribe a fixed degree distribution P(k), representing the exact number of contacts held by each individual agent, while connections between … Read more

🌐🔬 Small-World Network Agent-Based Models: Modeling Local Clustering and Global Reach

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Small-world network models provide a powerful Agent-Based Modeling (ABM) framework for infectious disease dynamics because they simultaneously capture two dominant features of real human contact systems: strong local clustering and short global separation. In this representation, individuals are modeled as nodes connected by links that reflect social or physical contacts. Most connections occur within tightly … Read more

🔗📈 Scale-Free Network Agent-Based Models: Modeling Epidemics in Heterogeneous Populations

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Scale-free network models represent a fundamental Agent-Based Modeling (ABM) framework for studying infectious disease dynamics in highly heterogeneous populations. In these models, individuals are represented as nodes connected by links that encode social or contact interactions. The defining feature of a scale-free network is its power-law degree distribution, in which a small number of nodes … Read more