Extended Compartmental Models (Multi-State/Specialized Flow)

🧬 Beyond Basic SIR: Advanced Compartmental Models for Public Health Interventions

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Standard epidemiological frameworks like SIR (Susceptible–Infectious–Removed) provide the foundational mathematics of disease spread. However, to evaluate non-pharmaceutical interventions (NPIs)—such as contact tracing, quarantine, and isolation—we must move beyond simple three-compartment structures. This post introduces two advanced frameworks essential for analyzing public health responses: These models provide a rigorous foundation for predicting outcomes when public health … Read more

💉 Modeling Vaccination Impact: The Susceptible–Vaccinated–Infectious–Recovered (SVIR) Framework

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The SVIR compartmental model extends the classical SIR structure to explicitly capture the dynamics of vaccination—an essential tool for evaluating public health interventions against infectious diseases. By integrating a vaccinated class, this framework enables rigorous quantification of how immunization campaigns alter transmission pathways, shift herd immunity thresholds, and inform optimal vaccine deployment strategies. 🗂️ Compartmental … Read more

🦠 Susceptible–Infectious–Recovered–Deceased (SIRD) Model

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The Susceptible–Infectious–Recovered–Deceased (SIRD) model is an extension of the classic SIR compartmental framework, with an explicit compartment for disease-induced mortality. This refinement addresses a key limitation of the basic SIR model, in which the single “Removed” (R) category lumped together individuals who recovered and those who died. By separating deaths into their own compartment (D), … Read more

🦠The SEIRS Model: Susceptible–Exposed–Infectious–Recovered–Susceptible

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🦠 Overview: Capturing Temporary Immunity. The SEIRS compartmental model extends the classic SIR framework by incorporating an Exposed (E) state (latency) and allowing Recovered (R) individuals to lose immunity and return to the Susceptible (S) pool after some time. In the standard SIR model, recovered individuals are permanently immune, which means SIR can describe one … Read more