Hand, foot, and mouth disease (HFMD) is a common childhood infectious disease. The incidence of HFMD has a pronounced seasonal tendency and is closely related to meteorological factors such as temperature, rainfall, and wind speed. In this paper, we propose a combined SARIMA-XGBoost model to improve the prediction accuracy of HFMD in 15 regions of Xinjiang, China. The SARIMA model is used for seasonal trends, and the XGBoost algorithm is applied for the nonlinear effects of meteorological factors. The geographical and temporal weighted regression model is designed to analyze the influence of meteorological factors from temporal and spatial perspectives. The analysis results show that the HFMD exhibits seasonal characteristics, peaking from May to August each year, and the HFMD incidence has significant spatial heterogeneity. The meteorological factors affecting the spread of HFMD vary among regions. Temperature and daylight significantly impact the transmission of the disease in most areas. Based on the verification experiment of forecasting, the proposed SARIMA-XGBoost model is superior to other models in accuracy, especially in regions with a high incidence of HFMD.

We continue with the systematic study of the speed of extinction of continuous-state branching processes in Lévy environments under more general branching mechanisms. Here, we deal with the weakly subcritical regime under the assumption that the branching mechanism is regularly varying. We extend recent results of Li and Xu (2018) and Palau et al. (2016), where it is assumed that the branching mechanism is stable, and complement the recent articles of Bansaye et al. (2021) and Cardona-Tobón and Pardo (2021), where the critical and the strongly and intermediate subcritical cases were treated, respectively. Our methodology combines a path analysis of the branching process together with its Lévy environment, fluctuation theory for Lévy processes, and the asymptotic behaviour of exponential functionals of Lévy processes. Our approach is inspired by the last two previously cited papers, and by Afanasyev et al. (2012), where the analogue was obtained.

The purpose of this study is to present a subgeometric convergence formula for the stationary distribution of the finite-level M/G/1-type Markov chain when taking its infinite-level limit, where the upper boundary level goes to infinity. This study is carried out using the fundamental deviation matrix, which is a block-decomposition-friendly solution to the Poisson equation of the deviation matrix. The fundamental deviation matrix provides a difference formula for the respective stationary distributions of the finite-level chain and the corresponding infinite-level chain. The difference formula plays a crucial role in the derivation of the main result of this paper, and the main result is used, for example, to derive an asymptotic formula for the loss probability in the MAP/GI/1/N queue.

In this paper, we consider a nonstandard multidimensional risk model, in which the claim sizes $\{\vec{X}_k, k\ge 1\}$ form an independent and identically distributed random vector sequence with dependent components. By assuming that there exists the regression dependence structure between inter-arrival time and the claim-size vectors, we extend the regression dependence to a more practical multidimensional risk model. For the univariate marginal distributions of claim vectors with consistently varying tails, we obtain the precise large deviation formulas for the multidimensional risk model with the regression size-dependent structure.

Mortality at older ages varies by season, increasing the uncertainty associated with modelling and projecting mortality at older ages and ultimately contributing to pension providers’ overall risk. As the population ages, it becomes more important to understand variations in seasonal mortality between pensioners and to identify those most vulnerable to seasonal mortality differences. Using data from the Self-Administered Pension Schemes mortality investigation of the Continuous Mortality Investigation of the Institute and Faculty of Actuaries, UK, this paper investigates variations in seasonal mortality amongst members of UK occupational pension schemes over the period 2000–2016. Results are also compared with the corresponding population of England and Wales. For the oldest age groups (80+), which are most affected by seasonality, females are more vulnerable to seasonal differences in mortality for each pensioner group relative to males. Following a long-term decline in the winter-summer mortality gap the gap increased over the period, particularly for female pensioners and dependants. Seasonality remains a feature of UK mortality at older ages and risk management for pension schemes should consider seasonality when analysing overall mortality experience.