models

Various tools for investigate the data in this data portal or models

🏠 The Household SIR Model: Bridging Micro-Scale Contacts and Macro-Scale Spread 📈

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🧬 Overview and Conceptual Motivation Classical epidemic models typically assume a well-mixed population in which every individual has an equal probability of contacting any other. The Household SIR model relaxes this assumption by introducing a realistic social hierarchy. Transmission is concentrated within small, intimate clusters such as households, while interactions across the broader community occur … Read more

📈 The Gompertz Growth Model: Capturing Asymptotic Deceleration in Epidemic Spread 📉

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🧬 Overview and Conceptual Motivation Within the broad spectrum of mathematical approaches to epidemic analysis, the Gompertz Growth Epidemic Model occupies a distinctive position as a phenomenological framework. Rather than explicitly modeling interactions between susceptible and infectious individuals, this model focuses on the observed growth trajectory of cumulative cases. Its defining feature is that the … Read more

📈 From Random Encounters to Deterministic Laws: The Gillespie Stochastic SIR and Its Mean-Field Limit 🎲

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🧬 Overview and Conceptual Motivation In infectious disease modeling, a central challenge is linking random, individual-level interactions to predictable population-level dynamics. The Gillespie stochastic SIR model provides a microscopic perspective in which each infection and recovery occurs as a discrete random event. This formulation captures chance effects that dominate when case numbers are small. As … Read more

📈 The Generalized SEIR Model: Capturing Complexity via Multi-Stage Latency 🧬

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🧬 Overview and Conceptual Motivation In infectious disease modeling, the transition from an exposed (latent) state to an infectious state is rarely instantaneous or memoryless. The Generalized SEIR model with multi-stage latency extends the classical SEIR framework by subdividing the latent period into multiple sequential stages. This structure, commonly referred to as the Method-of-Stages, allows … Read more

📈 The Foundations of Modern Epidemiology: The General Kermack–McKendrick ODE Model 🧬

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🧬 Overview and Conceptual Motivation The General Epidemic Model, commonly known as the Kermack–McKendrick model in ordinary differential equation form, is the foundational framework of mathematical epidemiology. Introduced in 1927, this model established a mechanistic description of disease transmission, moving the field beyond purely statistical curve fitting. A central result of this framework is the … Read more

📈 The Gamma-Distributed Infectious Period SIR Model: Precision Dynamics via the Method-of-Stages 🧬

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Standard epidemiological models often assume that the time an individual spends in an infectious state follows an exponential distribution, implying that most people recover almost immediately after infection. However, biological reality suggests that recovery times are more “peaked” around a mean. The Gamma-distributed infectious period SIR model—listed as a specialized framework in the sources—addresses this … Read more

📈 Frequency-Dependent Incidence: Modeling Transmission in Saturated Networks 🦠

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🧬 Overview and Conceptual Motivation In infectious disease modeling, the choice of the incidence function fundamentally shapes how transmission risk is represented. The Frequency-Dependent Incidence SIR model, also known as the Standard Incidence model, is designed for settings in which the number of contacts an individual makes per unit time is independent of total population … Read more

📈 The Exposed Class: Modeling the Invisible Latency of Infection 🧬

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🧬 Overview and Conceptual Motivation In the structure of modern epidemiological theory, the Exposed-class SEIR model represents a fundamental extension of the classical SIR framework. Unlike simpler models that assume individuals become immediately infectious after exposure, this formulation explicitly incorporates a latent period through the Exposed (E) compartment. This addition is essential for accurately representing … Read more

📈 The Erlang SEIR Model: Refining Epidemic Timing via the Method-of-Stages 🧬

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🧬 Overview and Conceptual Motivation In advanced epidemiological modeling, the common assumption that individuals transition between disease states at a constant rate implies a memoryless exponential distribution for the time spent in each compartment. This assumption often fails to reflect biological reality. The Erlang SEIR model, also known as the Method-of-Stages, addresses this limitation by … Read more

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

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🧬 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