ObjectivesTo investigate changes in daily mental health (MH) service use and mortality in response to the introduction and the lifting of the COVID-19 ‘lockdown’ policy in Spring 2020.DesignA regression discontinuity in time (RDiT) analysis of daily service-level activity.Setting and participantsMental healthcare data were extracted from 10 UK providers.Outcome measuresDaily (weekly for one site) deaths from all causes, referrals and discharges, inpatient care (admissions, discharges, caseloads) and community services (face-to-face (f2f)/non-f2f contacts, caseloads): Adult, older adult and child/adolescent mental health; early intervention in psychosis; home treatment teams and liaison/Accident and Emergency (A&E). Data were extracted from 1 Jan 2019 to 31 May 2020 for all sites, supplemented to 31 July 2020 for four sites. Changes around the commencement and lifting of COVID-19 ‘lockdown’ policy (23 March and 10 May, respectively) were estimated using a RDiT design with a difference-in-difference approach generating incidence rate ratios (IRRs), meta-analysed across sites.ResultsPooled estimates for the lockdown transition showed increased daily deaths (IRR 2.31, 95% CI 1.86 to 2.87), reduced referrals (IRR 0.62, 95% CI 0.55 to 0.70) and reduced inpatient admissions (IRR 0.75, 95% CI 0.67 to 0.83) and caseloads (IRR 0.85, 95% CI 0.79 to 0.91) compared with the pre lockdown period. All community services saw shifts from f2f to non-f2f contacts, but varied in caseload changes. Lift of lockdown was associated with reduced deaths (IRR 0.42, 95% CI 0.27 to 0.66), increased referrals (IRR 1.36, 95% CI 1.15 to 1.60) and increased inpatient admissions (IRR 1.21, 95% CI 1.04 to 1.42) and caseloads (IRR 1.06, 95% CI 1.00 to 1.12) compared with the lockdown period. Site-wide activity, inpatient care and community services did not return to pre lockdown levels after lift of lockdown, while number of deaths did. Between-site heterogeneity most often indicated variation in size rather than direction of effect.ConclusionsMH service delivery underwent sizeable changes during the first national lockdown, with as-yet unknown and unevaluated consequences.

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This paper addressed the robust stabilization performance of Tagaki-Sugeno (T-S) fuzzy systems under a state feedback controller. To attain this, an integral inequality is proposed by rearranging the quadratic matrix-vector form combined with Jensen's inequality to handle the single integral terms obtained by taking the derivative of the concerned Lyapunov-Krasovskii functional (LKF). By employing this integral inequality and by using integral inequality techniques, some improved delay dependent stability and stabilization results are established in terms of linear matrix inequalities for the proposed T-S fuzzy model. Finally some numerical examples are provided to facilitate the feasibility and less conservativeness of the proposed theoretical results.