A mathematical model for the transmission dynamics of silicosis in a mining environment is designed and its qualitative analysis is given. The model takes into account the severity of silica dust exposure in a mining environment. The whole analysis is done in both fractional differentiation and classical integer calculus. In the former case, the Haar wavelet numerical scheme is used to solve the model and perform graphical representations. In the integer calculus case, it is shown that the disease free and endemic equilibria are globally asymptotically stable in the absence as well as in the presence of silica dust particles in the air, respectively. The epidemiological implications of these results are discussed. Numerical simulations are presented to support the theoretical analysis. In fractional differentiation, we show graphically via the Haar wavelet scheme the convergence to the disease free-equilibrium and the global stability of the endemic equilibrium, results successfully confirmed analytically via the classical integer analysis.

设计了采矿环境中矽肺病传播动力学的数学模型，并进行了定性分析。该模型考虑了采矿环境中二氧化硅粉尘暴露的严重性。整个分析都是在分数微分和经典整数演算中完成的。在前一种情况下，将Haar小波数值方案用于求解模型并执行图形表​​示。在整数演算的情况下，表明在空气中不存在和存在二氧化硅尘埃颗粒的情况下，无病和地方病平衡分别全局渐近稳定。这些结果的流行病学意义进行了讨论。提出了数值模拟以支持理论分析。在分数微分中