A global Carleman estimate in a transmission wave equation and application to a one-measurement inverse problem

We consider a transmission wave equation in two embedded domains in $R^2$, where the speed is $a1 > 0$ in the inner domain and $a2 > 0$ in the outer domain. We prove a global Carleman inequality for this problem under the hypothesis that the inner domain is strictly convex and $a1 > a2$ . As a consequence of this inequality, uniqueness and Lip- schitz stability are obtained for the inverse problem of retrieving a stationary potential for the wave equation with Dirichlet data and discontinuous principal coefficient from a single time-dependent Neumann boundary measurement

Tracking health system performance in times of crisis using routine health data: lessons learned from a multicountry consortium

COVID-19 has prompted the use of readily available administrative data to track health system performance in times of crisis and to monitor disruptions in essential healthcare services. In this commentary we describe our experience working with these data and lessons learned across countries. Since April 2020, the Quality Evidence for Health System Transformation (QuEST) network has used administrative data and routine health information systems (RHIS) to assess health system performance during COVID-19 in Chile, Ethiopia, Ghana, Haiti, Lao People's Democratic Republic, Mexico, Nepal, South Africa, Republic of Korea and Thailand. We compiled a large set of indicators related to common health conditions for the purpose of multicountry comparisons. The study compiled 73 indicators. A total of 43% of the indicators compiled pertained to reproductive, maternal, newborn and child health (RMNCH). Only 12% of the indicators were related to hypertension, diabetes or cancer care. We also found few indicators related to mental health services and outcomes within these data systems. Moreover, 72% of the indicators compiled were related to volume of services delivered, 18% to health outcomes and only 10% to the quality of processes of care. While several datasets were complete or near-complete censuses of all health facilities in the country, others excluded some facility types or population groups. In some countries, RHIS did not capture services delivered through non-visit or nonconventional care during COVID-19, such as telemedicine. We propose the following recommendations to improve the analysis of administrative and RHIS data to track health system performance in times of crisis: ensure the scope of health conditions covered is aligned with the burden of disease, increase the number of indicators related to quality of care and health outcomes; incorporate data on nonconventional care such as telehealth; continue improving data quality and expand reporting from private sector facilities; move towards collecting patient-level data through electronic health records to facilitate quality-of-care assessment and equity analyses; implement more resilient and standardized health information technologies; reduce delays and loosen restrictions for researchers to access the data; complement routine data with patient-reported data; and employ mixed methods to better understand the underlying causes of service disruptions