MATLAB Implementation of SIR Epidemic Modeling with Code Description

The SIR model is one of the most fundamental mathematical frameworks in infectious disease dynamics, classifying populations into three compartments: Susceptible (S), Infected (I), and Recovered (R). It describes disease transmission through a system of differential equations. Implementing the SIR model in MATLAB typically involves the following key steps: Parameter Definition and Initialization Initialize key epidemiological parameters including initial susceptible proportion (S0), infected proportion (I0), recovered proportion (R0), transmission rate (β), and recovery rate (γ). These parameters directly govern the model's dynamic behavior and should be defined as numeric variables in MATLAB workspace. Differential Equation Construction The core implementation involves establishing three coupled ordinary differential equations (ODEs): - Susceptible change rate is inversely proportional to current susceptible and infected populations - Infected change rate incorporates both new infections and recovery transitions - Recovered change rate directly relates to the infected population's recovery speed In MATLAB code, this is typically implemented as a function returning a column vector [dS/dt; dI/dt; dR/dt] using element-wise operations. Numerical Solution Employ built-in solvers like ode45 to handle the ODE system. This solver uses adaptive Runge-Kutta methods with automatic step-size control for numerical stability. The implementation requires defining a time span (e.g., 100-day simulation) and passing the initial condition vector [S0; I0; R0] to the solver function. Result Visualization Use MATLAB's plot function to display three curves showing compartment evolution over time. Enhance graphical clarity by adding legends (legend function), axis labels (xlabel/ylabel), and differentiating curves through line style/color modifications. The hold on command enables overlapping multiple trajectories. Model Extension Directions - Incorporate birth/death rates to develop SIRS model with waning immunity - Add exposed compartment (E) to create SEIR model accounting for incubation periods - Implement spatial heterogeneity using cellular automata frameworks These extensions require modifying the ODE system and potentially using PDE solvers for spatial models. Typical applications include evaluating quarantine effectiveness, predicting epidemic peak timing, and analyzing vaccination coverage impacts. Practical implementations necessitate parameter calibration (β and γ) using historical data through optimization techniques like fminsearch or lsqcurvefit.