The resurgence and outbreaks of mumps occur frequently in many countries worldwide in recent years, even in countries with high vaccination coverage. In this study, a descriptive and spatiotemporal clustering analysis at the township level was conducted to explore the dynamic spatiotemporal aggregation and epidemiological characteristics of mumps in Wuhan. During 2005 and 2019, there were 40 685 cases reported in Wuhan, with an average annual morbidity of 28.11 per 100 000 populations. The morbidity showed a fluctuating tendency, and peaked in 2010 and 2018. Bimodal seasonality was found, with a large peak between May and July, and a mild peak from November to January in the following year. Male students aged 5–9-year-old were the main risk group of mumps infection. Significant global spatial auto-correlation was detected except in 2007, 2009 and 2015. The spatial and temporal scan statistics indicated that the hot-spots mainly located at the western and southern areas of Wuhan with variations almost every year. Our findings could assist the public health authorities to develop and improve targeted health strategies, and allocate health resources rationally.

The distributions for continuous, discrete, and conditional discrete scan statistics are studied. The approach of finite Markov chain imbedding, which has been applied to random permutations as well as to runs and patterns, is extended to compute the distribution of the conditional discrete scan statistic, defined from a sequence of Bernoulli trials. It is shown that the distribution of the continuous scan statistic induced by a Poisson process defined on (0, 1] is a limiting distribution of weighted distributions of conditional discrete scan statistics. Comparisons of rates of convergence as well as numerical comparisons of various bounds and approximations are provided to illustrate the theoretical results.

Locating activity hotspots – areas of higher density, more intense use, or distinct social units – is a prerequisite for answering many questions in animal ecology. However, for many species, carrying out such research from direct observations in tropical habitat is time-consuming and unrealistic for non-habituated animals. This study aimed to locate chimpanzee home ranges from transect nest counts. For validation purposes, 233 line transects were sampled within the home ranges of four habituated social groups of chimpanzees in Taï National Park, Côte d'Ivoire. In total, 373 km of transects were surveyed over 188 days and 683 nests of chimpanzee were recorded. First, we characterized heterogeneity of nest distribution patterns, including variation in density and group size within the area. Second, we used scan statistics, a likelihood-based cluster technique to locate chimpanzee social groups and compared them with the known home range boundaries. Chimpanzee nest distribution was characterized by a positive density and group-size gradient away from the range periphery. Furthermore, nest distribution clusters corresponding to the four groups could be successfully identified, although additional clusters for, for example, low-density areas between social groups seem to be an unavoidable by-product. The approach taken can be extended to a wide spectrum of data stemming from direct observations, camera traps, acoustic or genetic sampling to derive information about structure and patchiness of wild animal populations.

Let {Xi}i=1n be a sequence of random variables with two possible outcomes, denoted 0 and 1. Define a random variable Sn,m to be the maximum number of 1s within any m consecutive trials in {Xi}i=1n. The random variable Sn,m is called a discrete scan statistic and has applications in many areas. In this paper we evaluate the distribution of discrete scan statistics when {Xi}i=1n consists of exchangeable binary trials. We provide simple closed-form expressions for both conditional and unconditional distributions of Sn,m for 2m ≥ n. These results are also new for independent, identically distributed Bernoulli trials, which are a special case of exchangeable trials.

In this paper we examine the extremal tail probabilities of moving sums in a marked Poisson random field. These sums are computed by adding up the weighted occurrences of events lying within a scanning set of fixed shape and size. We also provide an alternative representation of the constants of the asymptotic formulae in terms of the occupation measure of the conditional local random field at zero, and extend these representations to the constants of asymptotic tail probabilities of Gaussian random fields.