The present work deals with the construction, development, and analysis of a viable normalized predictor-corrector-type nonstandard finite difference scheme for the SEIR model concerning the transmission dynamics of measles. The proposed numerical scheme double refines the solution and gives realistic results even for large step sizes, thus making it economical when integrating over long time periods. Moreover, it is dynamically consistent with a continuous system and unconditionally convergent and preserves the positive behavior of the state variables involved in the system. Simulations are performed to guarantee the results, and its effectiveness is compared with well-known numerical methods such as Runge–Kutta (RK) and Euler method of a predictor-corrector type.

中文翻译：

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SEIR流行病模型的精确预测器-校正器类型非标准有限差分方案

目前的工作涉及针对麻疹传播动力学的SEIR模型的可行的归一化预测器-校正器类型的非标准有限差分方案的构建，开发和分析。所提出的数值方案对解决方案进行了双重完善，即使对于较大的步长，也能给出逼真的结果，因此在长时间积分时非常经济。而且，它与连续系统动态一致且无条件收敛，并保留了系统中所涉及的状态变量的积极行为。进行仿真以保证结果，并将其有效性与著名的数值方法（例如Runge–Kutta（RK）和预测器-校正器类型的Euler方法）进行比较。