We developed a computational tool to assess the risks of novel coronavirus outbreaks outside of China. We estimate the dependence of the risk of a major outbreak in a country from imported cases on key parameters such as: (i) the evolution of the cumulative number of cases in mainland China outside the closed areas; (ii) the connectivity of the destination country with China, including baseline travel frequencies, the effect of travel restrictions, and the efficacy of entry screening at destination; and (iii) the efficacy of control measures in the destination country (expressed by the local reproduction number $R_{\mathrm{loc}}$ ). We found that in countries with low connectivity to China but with relatively high $R_{\mathrm{loc}}$ , the most beneficial control measure to reduce the risk of outbreaks is a further reduction in their importation number either by entry screening or travel restrictions. Countries with high connectivity but low $R_{\mathrm{loc}}$ benefit the most from policies that further reduce $R_{\mathrm{loc}}$ . Countries in the middle should consider a combination of such policies. Risk assessments were illustrated for selected groups of countries from America, Asia, and Europe. We investigated how their risks depend on those parameters, and how the risk is increasing in time as the number of cases in China is growing.

In this Letter, a generalization of pairwise models to non-Markovian epidemics on networks is presented. For the case of infectious periods of fixed length, the resulting pairwise model is a system of delay differential equations, which shows excellent agreement with results based on stochastic simulations. Furthermore, we analytically compute a new ${\mathcal{R}}_0$-like threshold quantity and an analytical relation between this and the final epidemic size. Additionally, we show that the pairwise model and the analytic results can be generalized to an arbitrary distribution of the infectious times, using integro-differential equations, and this leads to a general expression for the final epidemic size. By showing the rigorous link between non-Markovian dynamics and pairwise delay differential equations, we provide the framework for a more systematic understanding of non-Markovian dynamics.

COVID-19 epidemic has been suppressed in Hungary due to timely non-pharmaceutical interventions, prompting a considerable reduction in the number of contacts and transmission of the virus. This strategy was effective in preventing epidemic growth and reducing the incidence of COVID-19 to low levels. In this report, we present the first epidemiological and statistical analysis of the early phase of the COVID-19 outbreak in Hungary. Then, we establish an age-structured compartmental model to explore alternative post-lockdown scenarios. We incorporate various factors, such as age-specific measures, seasonal effects, and spatial heterogeneity to project the possible peak size and disease burden of a COVID-19 epidemic wave after the current measures are relaxed.

Background: Precisely predicting the water levels of rivers is critical for planning and supporting flood hazard and risk assessments and maintaining navigation, irrigation, and water withdrawal for urban areas and industry. In Hungary, the water level of rivers has been recorded since the early nineteenth century, and various water level prediction methods were developed. The Discrete Linear Cascade Model (DLCM) has been used since 1980s. However, its performance is not always reliable under the current climate-driven hydrological changes. Therefore, we aimed to test machine learning algorithms to make 7-day ahead forecasts, choose the best-performing model, and compare it with the actual DLCM. Results: According to the results, the Long Short-Term Memory (LSTM) model provided the best results in all time horizons, giving more precise predictions than the Baseline model, the Linear or Multilayer Perceptron Model. Despite underestimating water levels, the validation of the LSTM model revealed that 68.5‒76.1% of predictions fall within the required precision intervals. Predictions were relatively accurate for low (≤ 239 cm) and flood stages (≥ 650 cm), but became less reliable for medium stages (240–649 cm). Conclusions: The LSTM model provided better results in all hydrological situations than the DLCM. Though, LSTM is not a novel concept, its encoder–decoder architecture is the best option for solving multi-horizon forecasting problems (or “Many-to-Many” problems), and it can be trained effectively on vast volumes of data. Thus, we recommend testing the LSTM model in similar hydrological conditions (e.g., lowland, medium-sized river with low slope and mobile channel) to get reliable water level forecasts under the rapidly changing climate and various human impacts. Graphical

Understanding the role of different age groups in disease transmission is crucial for designing effective intervention strategies. Age-structured epidemic models capture these dynamics through contact matrices, which describe interactions between subpopulations. However, empirical contact estimation is inherently prone to measurement noise, as survey responses vary systematically across age groups and are collected through heterogeneous channels. This imprecision introduces substantial uncertainty into epidemic predictions. In this study, we present the Age Group Sensitivity Analysis (AGSA) framework for quantifying how structural perturbations in age-specific contact patterns propagate to epidemic outcomes. AGSA integrates age-stratified epidemic models with Latin Hypercube Sampling (LHS) and Partial Rank Correlation Coefficient (PRCC) analysis to perform a systematic sensitivity assessment of age-specific interactions. A key novelty of our approach is a sensitivity aggregation technique that attributes the overall dispersion in epidemic outcomes to individual age groups. By identifying the groups whose contact variations contribute most to model variability, AGSA highlights where refined empirical data are most urgently needed. This provides a principled basis for targeted data collection efforts, thereby constraining epidemic forecasts and supporting the robust evaluation of age-specific public health interventions.