MATLAB Implementation of the SIS Epidemiological Model

The SIS model is a fundamental framework in epidemiological dynamics, particularly suitable for diseases where recovered individuals do not acquire immunity (such as common cold). This model categorizes the population into two compartments: Susceptible (S) and Infected (I), and describes their dynamic interactions through differential equations. Implementing the SIS model in MATLAB typically involves the following key components: Parameter Configuration Critical parameters including infection rate (β) and recovery rate (γ) must be defined, as they determine both the transmission speed and recovery duration. The basic reproduction number R0 = β/γ serves as the threshold for epidemic outbreak detection. In MATLAB implementation, these parameters are typically declared as global variables or passed as function arguments. Differential Equation Formulation The standard SIS model differential equations are: dS/dt = -βSI/N + γI dI/dt = βSI/N - γI where N represents the total population (S + I = N), ensuring population conservation. For MATLAB implementation, these equations are converted into a vector form compatible with ODE solvers. Numerical Solution Method MATLAB's built-in ODE solvers (such as ode45) are employed for numerical computation. This requires creating a derivative function file that returns the rate of change for each compartment. The implementation involves defining initial infection ratios and time span, then calling the solver with appropriate tolerances and step sizes. Result Visualization The output typically includes time-series plots showing the proportion of infected individuals over time. Threshold lines (e.g., R0=1) can be added to facilitate analysis. Parameter sensitivity studies can be conducted by adjusting β and γ values to observe curve morphology changes, helping understand parameter impacts on transmission dynamics. Extension possibilities include introducing stochastic perturbations to simulate real-world uncertainties, or expanding to spatial grid models to study geographical transmission patterns. Although structurally simple, the SIS model effectively demonstrates core epidemiological modeling concepts—using mathematical tools to quantify disease transmission dynamics. The MATLAB implementation typically involves creating modular functions for parameter setup, equation definition, numerical solving, and visualization to ensure code reusability and clarity.