Measles is a highly transmissible disease in children around the world. According to the World Health Organization (WHO), 73% of deaths of children were due to measles in 2018. This study describes the physical solution of the SIQR model for measles spread under the effect of natural delay amongst different compartments. By three different numerical techniques, the efficacies of solutions of the underlying system have been compared and a clear preference of nonstandard finite-difference (NSFD) scheme over the rest has been established. It has also been observed, on principle, that the NSFD formulation recovers all the essential traits of a continuous model namely the boundedness, positivity and stability of equilibriums of populations. The numerical results have also been supported by a very strong classical analysis of the model where the existence of a solution vector in explicit subsets of the function spaces has been guaranteed which leads to optimization of fixed-point methods.

麻疹是一种在全世界儿童中具有高度传染性的疾病。根据世界卫生组织 (WHO) 的数据，2018 年 73% 的儿童死亡是由麻疹引起的。本研究描述了 SIQR 模型在不同隔间之间自然延迟的影响下麻疹传播的物理解决方案。通过三种不同的数值技术，已经比较了基础系统的解的有效性，并确定了非标准有限差分 (NSFD) 方案相对于其他方案的明显偏好。原则上还观察到，NSFD 公式恢复了连续模型的所有基本特征，即种群平衡的有界性、积极性和稳定性。