SEIR Epidemic Spread Model Calculator

The SEIR Model SEIR is a compartmental model used in epidemiology to simulate how infectious diseases spread through a population. The population is divided into four groups: Susceptible (S) — can catch the disease. Exposed (E) — infected but not yet infectious (incubation period). Infectious (I) — can spread the disease. Recovered (R) — immune after recovery.

The Equations dS/dt = -beta * S * I / N. dE/dt = beta * S * I / N - sigma * E. dI/dt = sigma * E - gamma * I. dR/dt = gamma * I. Where beta is the transmission rate, sigma is the rate of progression from exposed to infectious (1/incubation period), gamma is the recovery rate (1/infectious period), and N is the total population.

R0 (Basic Reproduction Number) R0 represents how many people one infectious person will infect in a fully susceptible population. R0 = beta / gamma. If R0 > 1, the disease will spread. If R0 < 1, it will die out. Historical R0 values: measles (12-18), chickenpox (10-12), COVID-19 original strain (~2.5), seasonal influenza (1.2-1.4).

Herd Immunity Threshold The proportion of the population that needs to be immune to stop spread: HIT = 1 - 1/R0. For measles (R0=15): 93% need immunity. For COVID-19 original (R0=2.5): 60%. For seasonal flu (R0=1.3): 23%.

Model Limitations SEIR assumes homogeneous mixing (everyone contacts everyone equally), no births/deaths during the epidemic, permanent immunity after recovery, and constant parameters. Real epidemics are more complex, but SEIR provides valuable insight into epidemic dynamics and the effects of interventions.