On timeline of enhancing testing-capacity of COVID-19: A case study via an optimal replacement model

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.