Infectious Disease and Epidemic Calculator (SIR Model)

The SIR framework breaks a closed population into three distinct compartments: Susceptible (S), Infected (I), and Recovered (R). The sum of these fractions always equals 100% of the total population, expressed mathematically as: recovered + infected + susceptible = 1. Transmission is governed by the basic reproduction number (R0), which represents the average number of secondary infections generated by a single infected individual in a wholly susceptible population. In this model, R0 is calculated by dividing the average time it takes to recover by the time between contacts (R0 = time_recover / time_contact). Step-by-step simulations are then generated across a defined time horizon by dividing the total time by the desired number of data points, producing a comprehensive trajectory of the epidemic curve.

Imagine a town with a total population of 10,000 people experiencing a mild respiratory virus. Initially, we set our parameters as follows: a starting infected population of 10 individuals (0.001 fraction), a recovery time of 5 days, and a contact time yielding an R0 of 2.5. We choose to run our simulation over a total time of 60 days broken down into 30 data points, giving us a time step of 2 days. Using the SIR differential equations, the calculator tracks how susceptible individuals rapidly contract the virus, driving up the infected curve until herd immunity thresholds are approached, after which recoveries outpace new infections and the epidemic gradually subsides.

When running simulations, remember that the basic SIR model assumes a closed population with no births, deaths, or migration during the timeframe. Always calibrate your R0 value carefully based on empirical public health data for the specific pathogen in question. Keep time steps small enough to capture rapid exponential growth phases accurately without introducing numerical instability into your graphical output.