A mean field game model for COVID-19 with human capital accumulation

In this manuscript, we study a model of human capital accumulation during the spread of disease following an agent-based approach, where agents behave maximising their intertemporal utility. We assume that the agent interaction is of mean field type, yielding a mean field game description of the problem. We discuss how the analysis of a model including both the mechanism of change of species from one epidemiological state to the other and an optimisation problem for each agent leads to an aggregate behaviour that is not easy to describe, and that sometimes exhibits structural issues. Therefore we eventually propose and study numerically a SEIRD model in which the rate of infection depends on the distribution of the population, given exogenously as the solution to the mean field game system arising as the macroscopic description of the discrete multi-agent economic model for the accumulation of human capital. Such a model arises in fact as a simplified but tractable version of the initial one

Quality of life and satisfaction of patients after oncoplastic or traditional breast-conserving surgery using the BREAST-Q (BCT module): a prospective study

Introduction: The oncoplastic conservative surgery was developed as a natural evolution of traditional surgery, attempting to improve the therapeutic and aesthetic outcomes where tumor resection could be followed by not-adequate results. Our primary aim is to evaluate how patient satisfaction and quality-of-life after conservative oncoplastic surgery, using BREAST-Q (BCT Module), change pre- and post-operatively. The secondary aim is to compare patient-reported outcome after oncoplastic or traditional conservative surgery. Patients and methods: We enrolled 647 patients who underwent traditional conservative surgery or oncoplastic surgery from January 2020 to December 2022. Only 232 women (35.9%) completed the BREAST-Q questionnaire on a web-based platform, at the preoperative phase and 3 months after treatment. Results: The average score of "Psychosocial well-being" and "Satisfaction with Breasts" 3 months after surgery showed a statistically significant improvement, while the average score for "Physical well-being: Chest" at 3 months showed a worsening compared to the baseline. "Sexual well-being" did not show statistically significant change. A significant difference between the post-operative outcome of oncoplastic surgery and traditional surgery was observed only for Physical well-being (better for traditional surgery). Conclusions: The study showed significant improvement in patient-reported outcomes 3 months after the surgery, except for physical discomfort that increases especially after oncoplastic surgery. Furthermore, our data, as well as many others, point to the appropriateness of using OCS where there is an effective indication, while the perspective of patients cannot find significant superiority over TCS in any of the areas analyzed

Development of a novel nomogram-based online tool to predict axillary status after neoadjuvant chemotherapy in cN+ breast cancer: A multicentre study on 1,950 patients

Background: Type of axillary surgery in breast cancer (BC) patients who convert from cN + to ycN0 after neoadjuvant chemotherapy (NAC) is still debated. The aim of the present study was to develop and validate a preoperative predictive nomogram to select those patients with a low risk of residual axillary disease after NAC, in whom axillary surgery could be minimized. Patients and methods: 1950 clinically node-positive BC patients from 11 Breast Units, treated by NAC and subsequent surgery, were included from 2005 to 2020. Patients were divided in two groups: those who achieved nodal pCR vs. those with residual nodal disease after NAC. The cohort was divided into training and validation set with a geographic separation criterion. The outcome was to identify independent predictors of axillary pathologic complete response (pCR). Results: Independent predictive factors associated to nodal pCR were axillary clinical complete response (cCR) after NAC (OR 3.11, p < 0.0001), ER-/HER2+ (OR 3.26, p < 0.0001) or ER+/HER2+ (OR 2.26, p = 0.0002) or ER-/HER2- (OR 1.89, p = 0.009) BC, breast cCR (OR 2.48, p < 0.0001), Ki67 > 14% (OR 0.52, p = 0.0005), and tumor grading G2 (OR 0.35, p = 0.002) or G3 (OR 0.29, p = 0.0003). The nomogram showed a sensitivity of 71% and a specificity of 73% (AUC 0.77, 95%CI 0.75\u20130.80). After external validation the accuracy of the nomogram was confirmed. Conclusion: The accuracy makes this freely-available, nomogram-based online tool useful to predict nodal pCR after NAC, translating the concept of tailored axillary surgery also in this setting of patients

Highly specialized Breast Centers did not experience delay of care during COVID-19 pandemic in Italy: the Senonetwork experience

The study aims to evaluate the performance of selected, high-volume, highly specialized, Italian Breast Centers at the time of COVID-19 pandemic (year 2020), compared to pre-pandemic time (year 2019), highlighting differences in terms of clinical presentation of breast cancer (BC) and therapeutic strategies

Preservation of Axillary Lymph Nodes Compared with Complete Dissection in T1–2 Breast Cancer Patients Presenting One or Two Metastatic Sentinel Lymph Nodes: The SINODAR-ONE Multicenter Randomized Clinical Trial

Background: The SINODAR-ONE trial is a prospective noninferiority multicenter randomized study aimed at assessing the role of axillary lymph node dissection (ALND) in patients undergoing either breast-conserving surgery or mastectomy for T1–2 breast cancer (BC) and presenting one or two macrometastatic sentinel lymph nodes (SLNs). The endpoints were to evaluate whether SLN biopsy (SLNB) only was associated with worsening of the prognosis compared with ALND in terms of overall survival (OS) and relapse. Methods: Patients were randomly assigned (1:1 ratio) to either removal of ≥ 10 axillary level I/II non-SLNs followed by adjuvant therapy (standard arm) or no further axillary treatment (experimental arm). Results: The trial started in April 2015 and ceased in April 2020, involving 889 patients. Median follow-up was 34.0 months. There were eight deaths (ALND, 4; SNLB only, 4), with 5-year cumulative mortality of 5.8% and 2.1% in the standard and experimental arm, respectively (p = 0.984). There were 26 recurrences (ALND 11; SNLB only, 15), with 5-year cumulative incidence of recurrence of 6.9% and 3.3% in the standard and experimental arm, respectively (p = 0.444). Only one axillary lymph node recurrence was observed in each arm. The 5-year OS rates were 98.9% and 98.8%, in the ALND and SNLB-only arm, respectively (p = 0.936). Conclusions: The 3-year survival and relapse rates of T1–2 BC patients with one or two macrometastatic SLNs treated with SLNB only, and adjuvant therapy, were not inferior to those of patients treated with ALND. These results do not support the use of routine ALND

Existence and non-existence for time-dependent mean field games with strong aggregation

We investigate the existence of classical solutions to second-order quadratic Mean-Field Games systems with local and strongly decreasing couplings of the form - σmα,α≥ 2 / N, where m is the population density and N is the dimension of the state space. We prove the existence of solutions under the assumption that σ is small enough. For large σ, we show that existence may fail whenever the time horizon T is large