About the SEIR Epidemic Model
This simulation is a particle-based realisation of the SEIR compartmental model from mathematical epidemiology. A population of 400 moving dots is divided into Susceptible, Exposed, Infectious and Recovered states. When an infectious dot comes within contact range of a susceptible one it may transmit the disease at a probability driven by the transmission rate β, while Exposed people incubate at rate σ and Infectious people recover at rate γ. The defining quantity is R₀ = β / γ.
The sliders set β (transmission), γ (recovery), σ (incubation), the starting vaccination share and the fraction of infectious people quarantined, and you can restart, pause and change the speed. The live chart plots every compartment over time and marks the herd-immunity threshold 1 − 1/R₀. Epidemiologists use exactly this structure to forecast hospital demand and design interventions for diseases from seasonal influenza to COVID-19 and Ebola.
Frequently Asked Questions
What is the SEIR model?
SEIR is a compartmental epidemic model that sorts a population into four states: Susceptible, Exposed (infected but not yet contagious), Infectious and Recovered. People flow from S to E to I to R over time. It extends the simpler SIR model by adding the Exposed stage to represent a disease's incubation period.
What does R₀ mean and why does 1 matter?
R₀, the basic reproduction number, is the average number of new infections caused by a single case in a fully susceptible population. Here it is computed as R₀ = β / γ. When R₀ is greater than 1 the outbreak grows; when it is below 1 it dies out, so the value 1 is the tipping point between a pandemic and extinction.
How does infection actually spread in this simulation?
Each infectious dot scans for nearby susceptible dots within a fixed contact radius. If a susceptible dot is close enough, it becomes Exposed with a probability proportional to the transmission rate β. Exposed dots later turn Infectious at rate σ, and Infectious dots recover at rate γ, gaining lifelong immunity.
What do the β, γ and σ sliders control?
β (transmission) sets how likely an infection is per close contact, so raising it makes the disease more contagious. γ (recovery) sets how fast infectious people recover; a higher γ shortens the infectious period and lowers R₀. σ (incubation) controls how quickly Exposed people become Infectious, governing the delay before the outbreak takes off.
What is herd immunity and where is it shown?
Herd immunity is the point at which enough of the population is immune that each case infects fewer than one other person, halting sustained spread. It is reached once a fraction 1 − 1/R₀ of people are immune. The chart draws this threshold as a dashed line, and the percentage rises as you increase R₀.
What does the Vaccination slider do?
The Vaccination % slider sets the share of the population that starts already immune, between 0 and 90 per cent. Vaccinated dots take no part in transmission, so increasing coverage removes susceptible targets and lowers the effective reproduction number. Pushing coverage past the herd-immunity threshold can stop an epidemic before it grows.
How does the Quarantine control work?
The Quarantine % slider isolates a fraction of infectious people by sharply reducing their movement. A quarantined infectious dot moves at roughly a tenth of normal speed, so it encounters far fewer susceptible dots and transmits less. This mimics case isolation, a core non-pharmaceutical intervention used in real outbreaks.
Is this simulation physically accurate?
It captures the qualitative behaviour of real SEIR dynamics, including exponential early growth, an epidemic peak, burnout and the herd-immunity threshold. It is a stochastic, individual-based approximation rather than a precise solution of the SEIR differential equations, and uses a small population of 400 with simplified random mixing, so exact numbers should be read as illustrative.
Why is the Exposed compartment important?
The Exposed compartment represents people who are infected but not yet contagious, reflecting a disease's incubation period. It introduces a lag between exposure and onward spread, which delays and can blunt the epidemic peak. Diseases with long incubation behave very differently from those that spread immediately, which is why SEIR is often preferred over plain SIR.
What happens when R₀ falls below 1?
When R₀ drops below 1, each infectious person infects fewer than one other on average, so the chain of transmission shrinks and the outbreak fades out. You can force this by lowering β, raising γ, vaccinating a large share, or quarantining infectious cases. The simulation colours the R₀ readout green once it falls below 1.
How is this used in the real world?
Public-health agencies use SEIR and related compartmental models to forecast case numbers, hospital and ICU demand, and the impact of measures such as vaccination, isolation and social distancing. During the 2014 West African Ebola outbreak, models with R₀ around 1.5 to 2 predicted explosive growth, and interventions that halved β were enough to suppress it.