This manuscript is devoted to a study of the existence and uniqueness of solutions to a mathematical model addressing the transmission dynamics of the coronavirus-19 infectious disease (COVID-19). The mentioned model is considered with a nonsingular kernel type derivative given by Caputo–Fabrizo with fractional order. For the required results of the existence and uniqueness of solution to the proposed model, Picard’s iterative method is applied. Furthermore, to investigate approximate solutions to the proposed model, we utilize the Laplace transform and Adomian’s decomposition (LADM). Some graphical presentations are given for different fractional orders for various compartments of the model under consideration.

该手稿致力于研究解决冠状病毒19传染病（COVID-19）传播动力学的数学模型的解决方案的存在和唯一性。考虑到上述模型具有由Caputo–Fabrizo给出的分数阶非奇异核类型导数。对于所提出的模型的解的存在性和唯一性的所需结果，采用了Picard的迭代方法。此外，为了研究提出的模型的近似解，我们利用了Laplace变换和Adomian分解（LADM）。对于所考虑的模型的各个部分，给出了针对不同分数阶的一些图形表示。