This manuscript is devoted to investigate qualitative theory of existence and uniqueness of the solution to a dynamical system of an infectious disease known as measles. For the respective theory, we utilize fixed point theory to construct sufficient conditions for existence and uniqueness of the solution. Some results corresponding to Hyers–Ulam stability are also investigated. Furthermore, some semianalytical results are computed for the considered system by using integral transform due to the Laplace and decomposition technique of Adomian. The obtained results are presented by graphs also.

中文翻译：

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传染病动力学系统的存在性理论和新颖的迭代方法

该手稿专门研究定性理论的存在性和唯一性，即对被称为麻疹的传染病动力学系统的解决方案。对于各自的理论，我们利用定点理论来构造解存在和唯一性的充分条件。还研究了与Hyers-Ulam稳定性相对应的一些结果。此外，由于Ladom和Adomian分解技术的影响，通过积分变换为所考虑的系统计算了一些半分析结果。所获得的结果也由图形表示。