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The COVID-19 pandemic has had a significant impact on countries worldwide, including the United Kingdom (UK). The UK has faced numerous challenges, but its response, including the rapid vaccination campaign, has been noteworthy. While progress has been made, the study of the pandemic is important to enable us to properly prepare for future epidemics. Collaboration, vigilance, and continued adherence to public health measures will be crucial in navigating the path to recovery and building resilience for the future. In this article, we propose an overview of the COVID-19 situation in the UK using both mathematical (a nonlinear differential equation model) and statistical (time series modeling on a moving window) models on the transmission dynamics of the COVID-19 virus from the beginning of the pandemic up until July 2022. This is achieved by integrating a hybrid model and daily empirical case and death data from the UK. We partition this dataset into before and after vaccination started in the UK to understand the influence of vaccination on disease dynamics. We used the mathematical model to present some mathematical analyses and the calculation of the basic reproduction number ( R 0 ). Following the sensitivity analysis index, we deduce that an increase in the rate of vaccination will decrease R 0 . Also, the model was fitted to the data from the UK to validate the mathematical model with real data, and we used the data to calculate time-varying R 0 . The homotopy perturbation method (HPM) was used for the numerical simulation to demonstrate the dynamics of the disease with varying parameters and the importance of vaccination. Furthermore, we used statistical modeling to validate our model by performing principal component analysis (PCA) to predict the evolution of the spread of the COVID-19 outbreak in the UK on some statistical predictor indicators from time series modeling on a 14-day moving window for detecting which of these indicators capture the dynamics of the disease spread across the epidemic curve. The results of the PCA, the index of dispersion, the fitted mathematical model, and the mathematical model simulation are all in agreement with the dynamics of the disease in the UK before and after vaccination started. Conclusively, our approach has been able to capture the dynamics of the pandemic at different phases of the disease outbreak, and the result presented will be useful to understand the evolution of the disease in the UK and future and emerging epidemics. [ABSTRACT FROM AUTHOR]

In this paper, we develop a deterministic mathematical epidemic model for tuberculosis outbreaks in order to study the disease's impact in a given population. We develop a qualitative analysis of the model by showing that the solution of the model is positive and bounded. The global stability analysis of the model uses Lyapunov functions and the threshold quantity of the model, which is the basic reproduction number is estimated. The existence and uniqueness analysis for Caputo fractional tuberculosis outbreak model is presented by transforming the deterministic model to a Caputo sense model. The deterministic model is used to predict real data from Uganda and Rwanda to see how well our model captured the dynamics of the disease in the countries considered. Furthermore, the sensitivity analysis of the parameters according to R 0 was considered in this study. The normalised forward sensitivity index is used to determine the most sensitive variables that are important for infection control. We simulate the Caputo fractional tuberculosis outbreak model using the Adams–Bashforth–Moulton approach to investigate the impact of treatment and vaccine rates, as well as the disease trajectory. Overall, our findings imply that increasing vaccination and especially treatment availability for infected people can reduce the prevalence and burden of tuberculosis on the human population. [ABSTRACT FROM AUTHOR]

In data mining, and statistics, anomaly detection is the process of finding data patterns (outcomes, values, or observations) that deviate from the rest of the other observations or outcomes. Anomaly detection is heavily used in solving real-world problems in many application domains, like medicine, finance, cybersecurity, banking, networking, transportation, and military surveillance for enemy activities, but not limited to only these fields. In this paper, we present an empirical study on unsupervised anomaly detection techniques such as Density-Based Spatial Clustering of Applications with Noise (DBSCAN), (DBSCAN++) (with uniform initialization, k-center initialization, uniform with approximate neighbor initialization, and k-center with approximate neighbor initialization), and k-means−− algorithms on six benchmark imbalanced data sets. Findings from our in-depth empirical study show that k-means−− is more robust than DBSCAN, and DBSCAN++, in terms of the different evaluation measures (F1-score, False alarm rate, Adjusted rand index, and Jaccard coefficient), and running time. We also observe that DBSCAN performs very well on data sets with fewer number of data points. Moreover, the results indicate that the choice of clustering algorithm can significantly impact the performance of anomaly detection and that the performance of different algorithms varies depending on the characteristics of the data. Overall, this study provides insights into the strengths and limitations of different clustering algorithms for anomaly detection and can help guide the selection of appropriate algorithms for specific applications. [ABSTRACT FROM AUTHOR]

The rising tide of smoking-related diseases has irreparably damaged the health of both young and old people, according to the World Health Organization. This study explores the dynamics of the age-structure smoking model under fractal-fractional (F-F) derivatives with government intervention coverage. We present a new fractal-fractional model for two-age structure smokers in the Caputo–Fabrizio framework to emphasize the potential of this operator. For the existence-uniqueness criterion of the given model, successive iterative sequences are defined with limit points that are the solutions of our proposed age-structure smoking model. We also use the functional technique to demonstrate the proposed model stability under the Ulam–Hyers condition. The two age-structure smoking models are numerically characterized using the Newton polynomial. We observe that in Groups 1 and 2, a change in the fractal-fractional orders has a direct effect on the dynamics of the smoking epidemic. Moreover, testing the inherent effectiveness of government interventions shows a considerable impact on potential, occasional, and temporary smokers when the fractal-fractional order is 0.95. It is the view that this study will contribute to the applicability of the schemes, the rich dynamics of the fractal, and the fractional perspective of future predictions. [ABSTRACT FROM AUTHOR]