Deterministic Models: The Foundation
This section explores foundational compartmental models like the SIR (Susceptible-Infectious-Removed) and SIRS (Susceptible-Infectious-Recovered-Susceptible) models. These models use differential equations to describe the flow of individuals between states, assuming large, well-mixed populations. They are crucial for understanding the core concept of the basic reproduction number, $R_0$, and the threshold conditions for an epidemic. Other important deterministic models include SEIR (Susceptible-Exposed-Infectious-Removed) for diseases with a latent period, and models incorporating vital dynamics (births/deaths) for endemic diseases.
Interactive SIR Epidemic Curve
SIR Controls
Basic Reproduction Number
5.0
Epidemic Occurs
SIRS Model: Temporary Immunity
This model (SIRS) includes a rate at which recovered individuals lose immunity and become susceptible again. This can lead to sustained oscillations or endemic states, unlike the basic SIR model.
SIRS Controls
SEIR Model: Latent Period
The SEIR model adds an 'Exposed' (E) compartment for diseases with a latent period, where individuals are infected but not yet infectious. This delays the onset of infectiousness.
SEIR Controls
SIR with Vital Dynamics: Endemic State
This SIR model includes constant birth and death rates. In such models, if $R_0 > 1$, the disease can become endemic, meaning it persists in the population indefinitely rather than dying out.
Vital Dynamics Controls
Spatial Models: Spread Across Landscapes
Spatial models analyze how diseases spread geographically. **Patch models** divide a region into discrete locations (e.g., cities) with travel between them. **PDE models** treat space as continuous, often describing disease spread as a "traveling wave." Both are crucial for understanding and controlling the geographic expansion of an epidemic.