Some Inverse Problems for the Burgers Equation and Related Systems

In this article we deal with one-dimensional inverse problems concerning the Burgers equation and some related nonlinear systems (involving heat effects and/or variable density). In these problems, the goal is to find the size of the spatial interval from some appropriate boundary observations of the solution. Depending on the properties of the initial and boundary data, we prove uniqueness and non-uniqueness results. In addition, we also solve some of these inverse problems numerically and compute approximations of the interval sizes

On the Controllability of Parabolic Systems with a Nonlinear Term Involving the State and the Gradient

We present some results concerning the controllability of a quasi-linear parabolic equation (with linear principal part) in a bounded domain of ${\mathbb R}^N$ with Dirichlet boundary conditions. We analyze the controllability problem with distributed controls (supported on a small open subset) and boundary controls (supported on a small part of the boundary). We prove that the system is null and approximately controllable at any time if the nonlinear term $f( y, \nabla y)$ grows slower than $|y| \log^{3/2}(1+ |y| + |\nabla y|) + |\nabla y| \log^{1/2}(1+ |y| + |\nabla y|)$ at infinity (generally, in this case, in the absence of control, blow-up occurs). The proofs use global Carleman estimates, parabolic regularity, and the fixed point method

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

Scaling up cancer care for children without medical insurance in developing countries: The case of Mexico

Background: In 2006, the Mexican government launched the Fund for Protection Against Catastrophic Expenditures (FPGC) to support financially healthcare of high cost illnesses. This study aimed at answering the question whether FPGC improved coverage for cancer care and to measure survival of FPGC affiliated children with cancer. Procedure A retrospective cohort study (2006–2009) was conducted in 47 public hospitals. Information of children and adolescents with cancer was analyzed. The coverage was estimated in accordance with expected number of incident cases and those registered at FPGC. The survival was analyzed by using Kaplan–Meier survival curves and Cox proportional hazards regression modeling. Results: The study included 3,821 patients. From 2006 to 2009, coverage of new cancer cases increased from 3.3% to 55.3%. Principal diagnoses were acute lymphoblastic leukemia (ALL, 46.4%), central nervous system (CNS) tumors (8.2%), and acute myeloid leukemia (AML, 7.4%). The survival rates at 36 months were ALL (50%), AML (30.5%), Hodgkin lymphoma (74.5%), Non-Hodgkin lymphoma (40.1%), CNS tumors (32.8%), renal tumors (58.4%), bone tumors (33.4%), retinoblastoma (59.2%), and other solid tumors (52.6%). The 3-year overall survival rates varied among the regions; children between the east and south-southeast had the higher risks (hazard ratio 3.0; 95% CI: 2.3–3.9) and 2.4; 95% CI: 2.0–2.8) of death from disease when compared with those from the central region. Conclusion: FPGC has increased coverage of cancer cases. Survival rates were different throughout the country. It is necessary to evaluate the effectiveness of this policy to increase access and identify opportunities to reduce the differences in survival

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

Health and working conditions of pregnant women working inside and outside the home in Mexico City

BACKGROUND: To explore differences related to health and working conditions by comparing socio-demographic parameters, reproductive and prenatal care characteristics and working conditions among pregnant women who are employed outside the home (extra-domestic) while still performing a domestic workload versus those who perform exclusively domestic work in the home (intra-domestic). METHODS: A cross-sectional study was carried out at Family Medicine Unit N 31 of the Mexican Institute of Social Security (IMSS) in Mexico City between April and July 2003. Interviews were conducted with 537 pregnant women engaged in either extra-domestic work plus intra-domestic tasks, or those performing strictly intra-domestic work. Information was obtained regarding their demographic status, prenatal care, reproductive, work characteristics, and health during pregnancy. RESULTS: One hundred ninety-six (36.5%) of the interviewed women had paid jobs outside the home in addition to domestic tasks, while three hundred forty-one (63.5 %) engaged in exclusively intra-domestic occupations. Of the women with paid jobs, 78.6% worked as clerks. Among domestic tasks, we found that the greatest workload was associated with washing of clothes, and our micro-ergonomic analysis revealed that women who worked strictly inside the home had a higher domestic workload versus employed women (69.2 vs. 44.9%). When we analyzed the effect of work on health during pregnancy, we observed that women who worked strictly inside the home were at a higher risk for musculoskeletal and genitourinary symptoms than those employed outside the home. CONCLUSION: These findings suggest that the effect of intra-domestic work should not be ignored when considering women's health during pregnancy, and that greater attention should be paid to women's working conditions during intra and extra-domestic work