CompartmentalModels

đź’‰ SIRDV Model: A Compartmental Epidemic Model with Vaccination and Mortality

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The Susceptible–Vaccinated–Infectious–Recovered–Deceased (SIRDV) model extends the classical SIR framework by incorporating prophylactic intervention through vaccination and disease-induced mortality. It improves realism by distinguishing between individuals who leave the susceptible compartment through infection or vaccination, and differentiates between those who recover and those who die from infection. 🔄 Compartmental Structure and Dynamics In the SIRDV model, … 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

🔄 The SIRS Compartmental Epidemic Model: Temporary Immunity and Endemic Cycles

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The Susceptible–Infectious–Recovered–Susceptible (SIRS) model extends the classic SIR framework by incorporating temporary immunity. After recovering, individuals transition to the Recovered (R) class, where they are immune for a period before returning to the Susceptible (S) pool. This reinfection cycle is ideal for modeling diseases like seasonal influenza, respiratory syncytial virus (RSV), or the common cold, … Read more

🔄 The SIS Compartmental Epidemic Model: Reinfection Without Immunity

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The Susceptible–Infectious–Susceptible (SIS) model is a classical framework used to describe the spread of infectious diseases that do not confer lasting immunity. Individuals transition between being susceptible (S) and infectious (I), with recovered individuals immediately returning to the susceptible class. This structure is appropriate for non-immunizing infections, such as the common cold, gonorrhea, or certain … Read more

🧪 The SEIR Compartmental Epidemic Model: Structure, Dynamics, and Extensions

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The Susceptible–Exposed–Infectious–Removed (SEIR) model is a classical and widely used framework in mathematical epidemiology. It extends the foundational SIR model by incorporating a latent (incubation) period during which individuals are infected but not yet infectious. This makes it more biologically realistic for diseases like measles, COVID-19, and influenza. The model has been extensively analyzed in … Read more