<p>This paper proposes an improved susceptible-infective-removed (SIR) model based on a discrete-time recursive method for predicting the spread of COVID-19-like infectious diseases. The model divides the population into three categories: susceptible (S), infected (I), and removed (R). By introducing dynamic infection rates (β) and removal rates (γ), a simplified, real-time, discrete-time recursive equation is established, replacing the traditional, computationally complex ordinary differential equations. The discrete-time recursive approach demonstrates particular suitability for the US healthcare reporting system, where daily case counts rather than continuous data streams are available for analysis. Actual epidemic data from Ohio state in the United States are used as a case study to validate the model’s effectiveness in short-term forecasting and long-term trend analysis. Results demonstrate that the model fits the epidemic curve well and accurately captures the dynamics of key transmission indicators, such as the basic reproduction number (R₀) and the effective reproduction number (R_e). Specifically, when R_e &gt; 1, the epidemic exhibits an explosive trend, while when R_e &lt; 1, the epidemic gradually subsides. Furthermore, the model quantitatively analyzes the effectiveness of different prevention and control measures (such as wearing masks and reducing social activities) on epidemic spread and explores the mathematical basis for the herd immunity threshold which is defined as the minimum proportion of immune individuals required to prevent sustained disease transmission. This mathematical model provides scientific support for public health decision-making, helps evaluate the effectiveness of prevention and control measures, and predicts epidemic trends. It also demonstrates the practical value of this mathematical model in responding to infectious disease emergencies.</p>