Three Mathematical Modeling Approaches for Infectious Diseases: SI, SIS, and SIR Models

Three fundamental mathematical models for infectious disease modeling are commonly used: SI, SIS, and SIR. The SI model simulates the transition between Susceptible and Infected populations only. The SIS model introduces a Recovered compartment where immunized individuals can become susceptible again, typically implemented using ordinary differential equations with reinfection parameters. The SIR model incorporates the progression from Infected to Recovered state, requiring numerical integration methods like Runge-Kutta for solving transmission dynamics.

This resource provides executable code implementations for all three models along with simulation plots demonstrating epidemic curves and phase transitions. The code architecture includes modular functions for parameter tuning (infection rate, recovery rate), initial condition setup, and visualization routines. Both beginners and professionals can benefit from studying the implementation details, which serve as foundation for more complex epidemiological models. For deeper theoretical understanding, refer to classical literature such as Kermack and McKendrick's seminal paper "A Contribution to the Mathematical Theory of Epidemics" which introduces fundamental reproduction number calculations.