A new approach to determine occupational accident dynamics by using ordinary differential equations based on SIR model

The motivation of this study is to develop and establish an occupational accident dynamical model (OA model) based on Susceptible-Infected-Recovered framework. In order to investigate the dynamics of the OA model, monthly occupational accident data from Turkey between 2013 and 2020 has been selected as dataset. The OA model is defined by a coupled first-order ordinary nonlinear differential equation with four variables. In addition, the relationships between these variables are described with ten parameters. The OA model's characterization of the equilibrium points is analyzed by investigating the behaviors of these points according to the eigenvalues derived from the Jacobian matrix. Also, the stability of these points is obtained according to the eigenvalues. These results show the behavior of the system near equilibrium points. After that, the reproduction number is computed by using the next-generation matrix method. The calculated reproduction number for given parameters reveals that the OA model is unstable. The OA model is numerically solved in 96 steps, with a time interval of 1 month, using the ODE45 Matlab routine based on the explicit Runge-Kutta algorithm. In addition, a modified OA model is developed by adding the Occupational Health and Safety (OHS) re-training parameter to the OA model to observe a reducing effect on occupational accident numbers. The main results of this study provide a new approach about the future estimation of the number of occupational accidents. Furthermore, through the comparison of numerical results from both models, the study demonstrates that national safety policies, particularly those enhancing the efficacy of OHS training, can effectively mitigate accidents.