We prove that for every tree $T$ of radius $h$, there is an integer $c$ such that every $T$-minor-free graph is contained in $H\boxtimes K_c$ for some graph $H$ with pathwidth at most $2h-1$. This is a qualitative strengthening of the Excluded Tree Minor Theorem of Robertson and Seymour (GM I). We show that radius is the right parameter to consider in this setting, and $2h-1$ is the best possible bound.

In this short report, we describe an outbreak of COVID-19 caused by Omicron subvariant BA.5.2.1 in highly vaccinated patients in a respiratory ward in a large acute general hospital in North West London, United Kingdom. The attack rate was high (14/33 (42%)) but the clinical impact was relatively non-severe including in patients who were at high risk of severe COVID-19. Twelve of fourteen patients had COVID-19 vaccinations. There was only one death due to COVID-19 pneumonitis. The findings of this outbreak investigation suggest that while the transmissibility of Omicron BA.5.2.1 subvariant is high, infections caused by this strain are non-severe in vaccinated patients, even if they are at high risk of severe COVID-19 infection.

Maternal syphilis not only seriously affects the quality of life of pregnant women themselves but also may cause various adverse pregnancy outcomes (APOs). This study aimed to analyse the association between the related factors and APOs in maternal syphilis. 7,030 pregnant women infected with syphilis in Henan Province between January 2016 and December 2022 were selected as participants. Information on their demographic and clinical characteristics, treatment status, and pregnancy outcomes was collected. Multivariate logistic regression models and chi-squared automatic interaction detector (CHAID) decision tree models were used to analyse the factors associated with APOs. The multivariate logistic regression results showed that the syphilis infection history (OR = 1.207, 95% CI, 1.035–1.409), the occurrence of abnormality during pregnancy (OR = 5.001, 95% CI, 4.203–5.951), not receiving standard treatment (OR = 1.370, 95% CI, 1.095–1.716), not receiving any treatment (OR = 1.313, 95% CI, 1.105–1.559), and a titre ≥1:8 at diagnosis (OR = 1.350, 95%CI, 1.079–1.690) and before delivery (OR = 1.985, 95%CI, 1.463–2.694) were risk factors. A total of six influencing factors of APOs in syphilis-infected women were screened using the CHAID decision tree model. Integrated prevention measures such as early screening, scientific eugenics assessment, and standard syphilis treatment are of great significance in reducing the incidence of APOs for pregnant women infected with syphilis.

We study the $R_\beta$-positivity and the existence of zero-temperature limits for a sequence of infinite-volume Gibbs measures $(\mu_{\beta}(\!\cdot\!))_{\beta \geq 0}$ at inverse temperature $\beta$ associated to a family of nearest-neighbor matrices $(Q_{\beta})_{\beta \geq 0}$ reflected at the origin. We use a probabilistic approach based on the continued fraction theory previously introduced in Ferrari and Martínez (1993) and sharpened in Littin and Martínez (2010). Some necessary and sufficient conditions are provided to ensure (i) the existence of a unique infinite-volume Gibbs measure for large but finite values of $\beta$, and (ii) the existence of weak limits as $\beta \to \infty$. Some application examples are revised to put in context the main results of this work.

Despite being a vaccine-preventable disease for decades, pertussis control is still a public health challenge. A pertussis outbreak emerged in Jerusalem (n = 257 cases, January to June 2023). Most cases were young children (median age 1.5 years), and 100 were infants under 1 year. The hospitalisation rate of infants was 24%, which was considerably higher than that of cases aged 1 year and above (3.8%). There was one fatality in an unvaccinated, 10-week-old infant whose mother had not received pertussis vaccination during pregnancy. Most children were unvaccinated and resided in Jewish ultra-orthodox neighbourhoods in Jerusalem district. An intervention programme and vaccination campaign are ongoing.

Fertility, particularly at its current low level in many developed countries and high level in some less developed countries, is a key factor driving demographic, economic, and societal changes at local, national, and global levels. Population ageing due to low fertility and increasing longevity represents one of the most significant global megatrends and risks. Many countries are already experiencing population decline and rapid growth of their elderly populations, with implications for workforce size, economic development, health and pension schemes, and social security arrangements. Actuaries are well known for their work on mortality and morbidity, but they have rarely considered fertility and its proximate determinants, despite their demographic and economic effects. This paper explores key explanations and outcomes of past and projected future fertility trends, and the implications for actuaries and for political and economic decision-makers.