Two-phase free boundary problems in convex domains

We study the regularity of minimizers of a two-phase free boundary problem. For a class of n-dimensional convex domains, we establish the Lipschitz continuity of the minimizer up to the fixed boundary under Neumann boundary conditions. Our proof uses an almost monotonicity formula for the Alt-Caffarelli-Friedman functional restricted to the convex domain. This requires a variant of the classical Friedland-Hayman inequality for geodesically convex subsets of the sphere with Neumann boundary conditions. To apply this inequality, in addition to convexity, we require a Dini condition governing the rate at which the fixed boundary converges to its limit cone at each boundary point.Comment: 34 page

Variola minor in England and Wales: the geographical course of a smallpox epidemic and the impediments to effective disease control, 1920–1935

The 1920–1935 epidemic of variola minor in England and Wales is a prime example of a major smallpox outbreak that spread in a national population with waning levels of vaccine-induced immunity. This paper examines the geographical course of the epidemic and the reasons why the disease was able to evade the (then) established protocols for smallpox control in many local government areas. The control issue is examined using archival records from the English county of Gloucestershire, where smallpox spread out of effective control in 1923. At the national level, our analysis demonstrates that the build-up (1920–1927) of the epidemic was characterised by a persistent core of reported cases of high intensity in the counties of central and northern England. Epidemic fade-out (1928–1935) was associated with an accelerated shift of disease activity to London and the southeast. Set against this national context, Gloucestershire represented a microcosm of the impediments to smallpox control in inter-war Britain. Here, a series of sociodemographic and administrative factors operated to impede disease control. Our study demonstrates the potential fragility of established disease control systems and the importance of professional and public cooperation, sometimes in the face of vehemently contested evidence over the nature of a disease and the means of its control, in attempts to limit the spread of epidemics

Mapping Alternative Impact: Alternative approaches to impact from co-produced research

No abstract available

Veterinarians’ knowledge and experience of avian influenza and perspectives on control measures in the UK

Background: The scale of the outbreak of highly pathogenic avian influenza (HPAI) in 2021–23 due to the influenza A/H5N1 virus is unprecedented. Methods: An online survey was designed to explore veterinarians’ experiences of and confidence in treating avian species, experiences of dealing with suspected HPAI and perspectives on control measures in the UK. The survey ran between December 2021 and March 2022. Results: Survey responses were received from 26 veterinarians. Although veterinarians are well placed to communicate HPAI-related information and guidance, a lack of confidence around treating birds and dealing with suspected cases of HPAI represent key barriers for non-specialist practices, and this limits opportunities to educate clients. Limitations: This study presents the views of a small group of self-selected respondents and may over-represent veterinarians with existing interests in avian species and/or avian influenza and who engage with online fora. Conclusions: Improved training and resources designed to increase confidence with avian species, along with guidance on diagnosing and reporting notifiable diseases, are needed for first opinion practices. Governing bodies should clarify regulations on treating birds in veterinary practices when HPAI outbreak numbers are high