To develop effective strategies for controlling the spread of the virus and potential future outbreaks, a deep understanding of disease transmission dynamics is crucial. This study proposes a modification to existing mathematical models used to describe the transmission dynamics of COVID-19 with environmental pathogens, incorporating a variable population, and employing incommensurate fractional order derivatives in ordinary differential equations. Our analysis accurately computes the basic reproduction number and demonstrates the global stability of the disease-free equilibrium point. Numerical simulations fitted to real data from South Africa show the efficacy of our proposed model, with fractional models enhancing flexibility. We also provide reliable values for initial conditions, model parameters, and order derivatives, and examine the sensitivity of model parameters. Our study provides valuable insights into COVID-19 transmission dynamics and has the potential to inform the development of effective control measures and prevention strategies.

翻译：为制定控制病毒传播及预防未来潜在暴发的有效策略，深入理解疾病传播动力学至关重要。本研究对现有描述环境病原体作用下COVID-19传播动力学的数学模型进行了改进，引入可变种群，并在常微分方程中采用了非一致分数阶导数。我们的分析精确计算了基本再生数，并证明了无病平衡点的全局稳定性。基于南非真实数据的数值模拟验证了所提模型的有效性，其中分数阶模型增强了灵活性。我们还提供了初始条件、模型参数及阶导数的可靠数值，并检验了模型参数的敏感性。本研究为COVID-19传播动力学提供了重要见解，有望为制定有效防控措施与预防策略提供依据。