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Many natural phenomena are quantified by counts of observable events, from the annihilation of quasiparticles in a lattice to predator-prey encounters on a landscape to spikes in a neural network. These events are triggered at random intervals when an underlying dynamical system occupies a set of reactive states in its phase space. We derive a general expression for the distribution of times between events in such counting processes assuming the underlying triggering dynamics is a stochastic process that converges to a stationary distribution. Our results contribute to resolving a long-standing dichotomy in the study of reaction-diffusion processes, showing the inter-reaction point process interpolates between a reaction- and a diffusion-limited regime. At low reaction rates, the inter-reaction process is Poisson with a rate depending on stationary properties of the event-triggering stochastic process. At high reaction rates, inter-reaction times are dominated by the hitting times to the reactive states. To further illustrate the power of this approach we apply our framework to obtain the counting statistics of two counting processes appearing in several biophysical scenarios. First, we study the common situation of estimating an animal's activity level by how often it crosses a detector, showing that the mean number of crossing events can decrease monotonically with the hitting rate, a seemingly 'paradoxical' result that could possibly lead to misinterpretation of experimental count data. Second, we derive the ensemble statistics for the detection of many particles, recovering and generalizing known results in the biophysics of chemosensation. Overall, we develop a unifying theoretical framework to quantify inter-event time distributions in reaction-diffusion systems that clarifies existing debates in the literature and provide examples of application to real-world scenarios., Comment: 14 pages, 3 figures

The emergence of a spatially-organized population distribution depends on the dynamics of the population and mediators of interaction (activators and inhibitors). Two broad classes of models have been used to investigate when and how self-organization is triggered, namely, reaction-diffusion and spatially nonlocal models. Nevertheless, these models implicitly assume smooth propagation scenarios, neglecting that individuals many times interact by exchanging short and abrupt pulses of the mediating substance. A recently proposed framework advances in the direction of properly accounting for these short-scale fluctuations by applying a coarse-graining procedure on the pulse dynamics. In this paper, we generalize the coarse-graining procedure and apply the extended formalism to new scenarios in which mediators influence individuals' reproductive success or their motility. We show that, in the slow- and fast-mediator limits, pulsed interactions recover, respectively, the reaction-diffusion and nonlocal models, providing a mechanistic connection between them. Furthermore, at each limit, the spatial stability condition is qualitatively different, leading to a timescale-induced transition where spatial patterns emerge as mediator dynamics becomes sufficiently fast.

Ecologists have long investigated how demographic and movement parameters determine the spatial distribution and critical habitat size of a population. However, most models oversimplify movement behavior, neglecting how landscape heterogeneity influences individual movement. We relax this assumption and introduce a reaction-advection-diffusion equation that describes population dynamics when individuals exhibit space-dependent movement bias toward preferred regions. Our model incorporates two types of these preferred regions: a high-quality habitat patch, termed `habitat', which is included to model avoidance of degraded habitats like deforested regions; and a preferred location, such as a chemoattractant source or a watering hole, that we allow to be asymmetrically located with respect to habitat edges. In this scenario, the critical habitat size depends on both the relative position of the preferred location and the movement bias intensities. When preferred locations are near habitat edges, the critical habitat size can decrease when diffusion increases, a phenomenon called the drift paradox. Also, ecological traps arise when the habitat overcrowds due to excessive attractiveness or the preferred location is near a low-quality region. Our results highlight the importance of species-specific movement behavior and habitat preference as drivers of population dynamics in fragmented landscapes and, therefore, in the design of protected areas., Comment: 21 pages, 8 figures

Efficient personnel scheduling plays a significant role in matching workload demand in organizations. However, staff scheduling is sometimes affected by unexpected events, such as the COVID-19 pandemic, that disrupt regular operations. Since infectious diseases like COVID-19 transmit mainly through close contact with individuals, an efficient way to prevent the spread is by limiting the number of on-site employees in the workplace along with regular testing. Thus, determining an optimal scheduling and testing strategy that meets the organization's goals and prevents the spread of the virus is crucial during disease outbreaks. In this paper, we formulate these challenges in the framework of two Mixed Integer Non-linear Programming (MINLP) models. The first model aims to derive optimal staff occupancy and testing strategies to minimize the risk of infection among employees, while the second model aims at only optimal staff occupancy under a random testing strategy. To solve the problems expressed in the models, we propose a canonical genetic algorithm as well as two commercial solvers. Using both real and synthetic contact networks of employees, our results show that following the recommended occupancy and testing strategy reduces the risk of infection 25\%--60\% under different scenarios., Comment: 15 pages, 2 figures

Human mobility contributes to the fast spatio-temporal propagation of infectious diseases. During an outbreak, monitoring the infection situation on either side of an international border is very crucial as there is always a higher risk of disease importation associated with cross-border migration. Mechanistic models are effective tools to investigate the consequences of cross-border mobility on disease dynamics and help in designing effective control strategies. However, in practice, due to the unavailability of cross-border mobility data, it becomes difficult to propose reliable, model-based strategies. In this study, we propose a method for estimating cross-border mobility flux between any pair of regions that share an international border from the observed difference in the timing of the infection peak in each region. Assuming the underlying disease dynamics is governed by a Susceptible-Infected-Recovered (SIR) model, we employ stochastic simulations to obtain the maximum likelihood cross-border mobility estimate for any pair of regions where the difference in peak time can be measured. We then investigate how the estimate of cross-border mobility flux varies depending on the disease transmission rate, which is a key epidemiological parameter. We further show that the uncertainty in mobility flux estimates decreases for higher disease transmission rates and larger observed differences in peak timing. Finally, as a case study, we apply the method to some selected regions along the Poland-Germany border which are directly connected through multiple modes of transportation and quantify the cross-border fluxes from the COVID-19 cases data during the period $20^{\rm th}$ February $2021$ to $20^{\rm th}$ June $2021$., Comment: Added Reference (Abdussalam et al. (2022) in Section 3

Throughout the coronavirus disease 2019 (COVID-19) pandemic, decision makers have relied on forecasting models to determine and implement non-pharmaceutical interventions (NPI). In building the forecasting models, continuously updated datasets from various stakeholders including developers, analysts, and testers are required to provide precise predictions. Here we report the design of a scalable pipeline which serves as a data synchronization to support inter-country top-down spatiotemporal observations and forecasting models of COVID-19, named the where2test, for Germany, Czechia and Poland. We have built an operational data store (ODS) using PostgreSQL to continuously consolidate datasets from multiple data sources, perform collaborative work, facilitate high performance data analysis, and trace changes. The ODS has been built not only to store the COVID-19 data from Germany, Czechia, and Poland but also other areas. Employing the dimensional fact model, a schema of metadata is capable of synchronizing the various structures of data from those regions, and is scalable to the entire world. Next, the ODS is populated using batch Extract, Transfer, and Load (ETL) jobs. The SQL queries are subsequently created to reduce the need for pre-processing data for users. The data can then support not only forecasting using a version-controlled Arima-Holt model and other analyses to support decision making, but also risk calculator and optimisation apps. The data synchronization runs at a daily interval, which is displayed at https://www.where2test.de., Comment: DECo@VLDB22: workshop paper accepted

Long-term care facilities have been widely affected by the COVID-19 pandemic. Retirement homes are particularly vulnerable due to the higher mortality risk of infected elderly individuals. Once an outbreak occurs, suppressing the spread of the virus in retirement homes is challenging because the residents are in contact with each other, and isolation measures cannot be widely enforced. Regular testing strategies, on the other hand, have been shown to effectively prevent outbreaks in retirement homes. However, high frequency testing may consume substantial staff working time, which results in a trade-off between the time invested in testing, and the time spent providing essential care to residents. Thus, developing an optimal testing strategy is crucial to proactively detect infections while guaranteeing efficient use of limited staff time in these facilities. Although numerous efforts have been made to prevent the virus from spreading in long-term care facilities, this is the first study to develop testing strategies based on formal optimization methods. This paper proposes two novel optimization models for testing schedules. The models aim to minimize the risk of infection in retirement homes, considering the trade-off between the probability of infection and staff workload. We employ a probabilistic approach in conjunction with the optimization models, to compute the risk of infection, including contact rates, incidence status, and the probability of infection of the residents. To solve the models, we propose an enhanced local search algorithm by leveraging the symmetry property of the optimal solution. We perform several experiments with realistically sized instances and show that the proposed approach can derive optimal testing strategies., Comment: 44 pages, 3 figures

During the COVID-19 pandemic, many organizations (e.g. businesses, companies, government facilities, etc.) have attempted to reduce infection risk by employing partial home office strategies. However, working from home can also reduce productivity for certain types of work and particular employees. Over the long term, many organizations therefore face a need to balance infection risk against productivity. Motivated by this trade-off, we model this situation as a bi-objective optimization problem and propose a practical approach to find trade-off (Pareto optimal) solutions. We present a new probabilistic framework to compute the expected number of infected employees as a function of key parameters including: the incidence level in the neighborhood of the organization, the COVID-19 transmission rate, the number of employees, the percentage of vaccinated employees, the testing frequency, and the contact rate among employees. We implement the model and the optimization algorithm and perform several numerical experiments with different parameter settings. Furthermore, we provide an online application based on the models and algorithms developed in this paper, which can be used to identify the optimal workplace occupancy rate for real-world organizations.