We prove a scaling limit theorem for two-type Galton–Watson branching processes with interaction. The limit theorem gives rise to a class of mixed-state branching processes with interaction used to simulate evolution for cell division affected by parasites. Such processes can also be obtained by the pathwise-unique solution to a stochastic equation system. Moreover, we present sufficient conditions for extinction with probability 1 and the exponential ergodicity in the $L^1$-Wasserstein distance of such processes in some cases.

In this paper, we introduce a unified framework based on the pathwise expansion method to derive explicit recursive formulas for cumulative distribution functions, option prices, and transition densities in multivariate diffusion models. A key innovation of our approach is the introduction of the quasi-Lamperti transform, which normalizes the diffusion matrix at the initial time. This transformation facilitates expansions using uncorrelated Brownian motions, effectively reducing multivariate problems to one-dimensional computations. Consequently, both the analysis and the computation are significantly simplified. We also present two novel applications of the pathwise expansion method. Specifically, we employ the proposed framework to compute the value-at-risk for stock portfolios and to evaluate complex derivatives, such as forward-starting options. Our method has the flexibility to accommodate models with diverse features, including stochastic risk premiums, stochastic volatility, and nonaffine structures. Numerical experiments demonstrate the accuracy and computational efficiency of our approach. In addition, as a theoretical contribution, we establish an equivalence between the pathwise expansion method and the Hermite polynomial-based expansion method in the literature.

In large public health jurisdictions, only a small proportion of people infected with Salmonella are interviewed due to resource constraints. As such, sources of illness are rarely found, and preventative action not implemented. We trialled alternative methods to contact notified salmonellosis cases to collect information on exposures and risks, focusing particularly on the feasibility of SMS (short message service)-based surveillance. Over five-years period we sequentially mailed letters, sent online surveys, and then text messages. The SMS approach was designed to assess the efficiency of a two-way personalized messaging model in gathering actionable public health data. The personalized SMS-follow-up model demonstrated the highest success: 56% of cases responded, enabling the identification and intervention of 10 distinct point-source outbreaks of Salmonella. SMS-based surveillance offers a novel, efficient, and acceptable method for collecting critical food exposure data in Salmonella cases. In settings where resources are constrained, SMS can complement traditional case follow-up methods, enhancing both the timeliness and effectiveness of outbreak detection. Integrating this follow-up with routine clinical care could further enhance the acceptance and success of this method. This study highlights the promise of SMS in streamlining surveillance efforts and warrants further exploration for application to other infectious diseases.

Embracing the potential of foresight in migration policy, North Macedonia has embarked on a ground-breaking journey to institutionalize anticipatory governance through extensive capacity-building activities, imparting foresight methods to stakeholders responsible for shaping migration policies. This research provides a comprehensive overview, detailing the initiative’s origins, alignment with the Resolution on Migration Policy 2021–2025, and the accompanying Action Plan. The study assesses the impact and potential of the Anticipatory Governance in Migration in North Macedonia when fully integrated with the action plan, which focuses on data-based management that oversees the migration policy resolution and the migration policy milieu. Through a comprehensive analysis of the foresight interventions, training programs, and stakeholder engagements, this study unveils the potential impact of forward-looking planning on North Macedonia’s migration policy landscape. The conclusion and recommendations have broader significance, extending beyond North Macedonia to serve as a model for other countries confronting migration challenges in our rapidly changing world.

We consider a population consisting of two types of individuals, each of which can produce offspring on two different islands (in particular, the islands can be interpreted as active or dormant individuals). We model the evolution of the population of each type using a two-type Feller diffusion with immigration and study the frequency of one type on each island, when the total population size on each island is forced to be constant at a dense set of times. This leads to the solution of a stochastic differential equation, which we call the asymmetric two-island frequency process. We derive properties of this process and obtain a large population limit as the total size of each island tends to infinity. Additionally, we compute the fluctuations of the process around its deterministic limit. We establish conditions under which the asymmetric two-island frequency process has a moment dual. The dual is a continuous-time two-dimensional Markov chain that can be interpreted in terms of mutation, branching, pairwise branching, coalescence, and a novel mixed selection–migration term.

This article proposes a novel method for estimating quantile regression models that account for sample selection. Unlike the approach by Arellano and Bonhomme (2017, Econometrica 85(1), 1–28; hereafter referred to as AB17), which employs a parametric selection equation, our method utilizes a standard binary quantile regression model to handle the selection issue, thereby accommodating general heterogeneity in both the selection and outcome equations. We adopt a semiparametric estimation technique for the outcome quantile regression by integrating local moment conditions, resulting in $\sqrt {n}$-consistent estimators for the quantile coefficients and copula parameter. Monte Carlo simulation results demonstrate that our estimator performs well in finite samples. Additionally, we apply our method to examine the wage distribution among women using a randomly simulated sample from the US General Social Survey. Our key finding is the presence of significant positive selection among women in the US, which is notably more pronounced than the estimates produced by the AB17’s model.

This paper examines an insurer’s optimal asset allocation and reinsurance policies. The financial market framework includes one risk-free and one risky asset. The insurer has two business lines, where the ordinary claim process is modeled by a compound Poisson process and catastrophic claims follow a compound dynamic contagion process. The dynamic contagion process, which is a generalization of the externally exciting Cox process with shot-noise intensity and the self-exciting Hawkes process, is enhanced by accommodating the dependency structure between the magnitude of contribution to intensity after initial events for catastrophic insurance products and its claim/loss size. We also consider the dependency structure between the positive effect on the intensity and the negative crashes on the risky financial asset when initial events occur. Our objective is to maximize the insurer’s expected utility of terminal surplus. We construct the extended Hamilton–Jacobi–Bellman (HJB) equation using dynamic programming principles to derive an explicit optimal reinsurance policy for ordinary claims. We further develop an iterative scheme for solving the value function and the optimal asset allocation policy and the reinsurance policy for catastrophic claims numerically, providing a rigorous convergence proof. Finally, we present numerical examples to demonstrate the impact of key parameters.

We investigated the potential yield of conducting active case finding for tuberculosis (TB) within a defined geographic radius (50 or 100 m) around the households of individuals diagnosed with TB at health facilities. In a well-defined geographic area within Kampala, Uganda, residential locations were determined for 85 people diagnosed with TB at local health facilities over an 18-month period and for 60 individuals diagnosed with TB during a subsequent community-wide door-to-door screening campaign. Ten of the individuals diagnosed through community screening lived within 50 m of an individual previously diagnosed with TB in a local health facility (TB prevalence: 0.98%), and 15 lived at a distance of 50–100 m (prevalence: 0.87%). The prevalence ratio was 1.4 (95% confidence interval (CI): 0.7–2.9) for those <50 m and 1.2 (95% CI 0.6–2.2) for those 50–100 m, compared to >100 m. Using TB notifications to identify areas for geographically targeted case finding is at most moderately more efficient than screening the general population in the context of urban Uganda.

Attaining the target of <0.1% HBsAg positives in children aged <5 years in vaccinated populations by 2030 is a WHO indicator of hepatitis B elimination. We aimed to calculate the prevalence of HBsAg- and anti-HBc-positive children and adolescents in the low-prevalence country of Germany. In total, 3567 children and adolescents aged 3–17 years participated in a national population based cross-sectional study. Data were collected between 2014 and 2017 using questionnaires and health examinations, including blood samples. Applying a weighted analysis to account for survey design and participant characteristics, we calculated the HBsAg and anti-HBc prevalence and described them by anti-HBs positivity. In total, 3007 participants had all three sero-markers measured. None were found HBsAg and anti-HBc positive. Seven (0.3%, 95% CI: 0.1–0.8) were anti-HBc positive and HBsAg negative; six were also anti-HBs positive. All anti-HBc-positive participants were aged ≥7 years and three had no migration background. Four anti-HBc-positive participants had known vaccination status; three had been vaccinated according to national recommendations. This very low hepatitis B virus sero-prevalence among children and adolescents indicates that Germany is reaching some hepatitis B virus elimination targets. We recommend maintaining preventive measures, in particular a high vaccination coverage, in order to reach hepatitis B elimination.

A company with n geographically widely dispersed sites seeks an insurance policy that pays off if m out of the n sites experience rarely occurring catastrophes (e.g., earthquakes) during a year. This study compares three strategies for an insurance company wishing to offer such an m-out-of-n policy, assuming the existence of markets for insurance on the individual sites with coverage periods of various lengths of a year or less. Strategy A is static: at the beginning of the year it buys a reinsurance policy on each individual site covering the entire year and makes no later adjustments. By contrast, Strategies S and C are dynamic and adaptive, exploiting the availability of individual-site policies for shorter periods than a year to make changes in the coverage on individual sites as quakes occur during the year. Strategy S uses the payoff from reinsurance when a quake occurs at a particular site to increase coverage for the remainder of the year on the sites that have not yet had quakes. Strategy C buys individual-site policies covering successive time periods of fixed length, observing the system at the beginning of each period and using cash on hand plus cash obtained from a reinsurance payoff (if any) during the previous period to decide how much cash to retain and how much reinsurance to purchase for the current period. The study relies on expected utility to determine indifference premiums and compare the premiums and loss probabilities for the three strategies.

The process to better understand the intricate evolution of our urban territories requires combining urban data from different or concurrent instances of time to provide stakeholders with more complete views of possible evolutions of a city. Geospatial rules have been proposed in the past to validate 3D semantic city models, however, there is a lack of research in the validation of multiple, concurrent and successive, scenarios of urban evolution. Using Semantic Web Ontologies and logical rules, we present a novel standards-based methodology for validating integrated city models. Using this methodology, we propose interoperable rules for validating integrated open 3D city snapshots used for representing multiple scenarios of evolution. We also implement a reproducible proof of concept test suite for applying the proposed rules. To illustrate how these contributions can be used in a real-world data validation use-case, we also provide example queries on the validated data. These queries are specifically used to construct a 3D web application for visualizing and analysing urban changes across multiple scenarios of evolution of a selected zone of interest.