Process of enhancing testing-capacity regarding COVID-19 is a topic of interest. This task of enhancing is constrained by socio-economic background of a country either in favorable or unfavorable ways. In this paper, we investigate timing of enhancing testing-capacity as an optimal problem, where the enhancement is quantified via number of tests as an instant measure and recovered portion as a long-term measure. The proposed work is structured analogous to an optimal machine replacement model based on a non-linear integral equation. Overall model is partially identifiable and compatible parameter estimations are carried out for a specific case study covering an early stage scenario. In addition, scenario development criteria on demand and effort for enhancing testing-capacity are introduced for predictions. In one numerical experiment, it is observed that frequency of enhancing testing-capacity starts decreasing after two increments indicating a favorable direction amidst effort constraints.

增强 COVID-19 检测能力的过程是一个有趣的话题。这种增强的任务受到一个国家的社会经济背景的限制，无论是有利的还是不利的。在本文中，我们将增强测试能力的时间作为一个最优问题进行研究，其中增强通过测试数量作为即时测量值进行量化，恢复部分作为长期测量值进行量化。拟议工作的结构类似于基于非线性积分方程的最佳机器更换模型。整体模型是部分可识别的，并且针对涵盖早期场景的特定案例研究进行了兼容参数估计。此外，还引入了按需情景开发标准和增强测试能力的努力以进行预测。在一项数值实验中，