Foundational Compartmental Models (Deterministic, ODE)

šŸ› The Andersonā€“May Macroparasite Model: Dynamics of Helminth Infection

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šŸ“ˆ Conceptual Overview In contrast to microparasite models, which track whether hosts are infected or not, the Andersonā€“May macroparasite model focuses on infections where disease severity and transmission depend on the parasite burden within individual hosts. This framework is essential for helminth infections such as hookworm, schistosomiasis, and lymphatic filariasis, where morbidity increases nonlinearly with … Read more

šŸ”„ The SIRS Compartmental Epidemic Model: Temporary Immunity and Endemic Cycles

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The Susceptibleā€“Infectiousā€“Recoveredā€“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

šŸ”„ The SIS Compartmental Epidemic Model: Reinfection Without Immunity

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The Susceptibleā€“Infectiousā€“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

šŸ§Ŗ The SEIR Compartmental Epidemic Model: Structure, Dynamics, and Extensions

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The Susceptibleā€“Exposedā€“Infectiousā€“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

šŸ¦  The Susceptibleā€“Infectiousā€“Removed (SIR) Model

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The Susceptibleā€“Infectiousā€“Removed (SIR) model is the foundational framework in mathematical epidemiology. Originally proposed by W. O. Kermack and A. G. McKendrick in 1927, this model provides a deterministic mechanism to analyze how infectious diseases evolve within a population over time. 1. Core Compartmental Structure The model partitions the total population (N) into three mutually exclusive … Read more