https://dspace.univ-adrar.edu.dz/jspui/handle/123456789/111 2026-10-24T17:06:34Z https://dspace.univ-adrar.edu.dz/jspui/handle/123456789/9386 Title: Mathematical analysis of a class of stochastic epidemic models Authors: MEDIANI, Mhammed; Slama, Abdeldjalil / Supervisor; Boudaoui, Ahmed / Co-supervisor Abstract: Over the past few decades, epidemics caused by highly pathogenic viruses such as the coronavirus, measles virus, and human immunodeficiency virus (HIV) have posed severe threats to public health. From a microscopic perspective, stochasticity plays a crucial role in viral replication, yet theoretical investigations of epidemic models incorporating biologically plausible stochastic effects remain limited. This thesis aims to address this gap by analyzing the evolutionary dynamics of stochastic epidemic models and assessing the impact of stochastic perturbations on viral pathogenesis and disease progression. In this work, we develop and study stochastic models that incorporate viral production mechanisms while integrating the Ornstein-Uhlenbeck or Black-Karasinski process. Specifically, we assume that key epidemiological parameters-such as the conversion rate from an eclipse phase to an infectious state—evolve according to the Ornstein-Uhlenbeck process. Within a well-defined mathematical framework, we establish and extend non-standard analytical approaches to demonstrate fundamental properties of these stochastic models, including the existence and uniqueness of global solutions, the presence of stationary distributions, and the conditions under which disease extinction occurs. Furthermore, we show that introducing stochastic perturbations in this manner is both mathematically rigorous and biologically justified. To support our theoretical findings, numerical simulations are conducted at the end of each section. These simulations validate the analytical results and illustrate the accuracy of the derived conditions and threshold parameters.; على مدار العقود القليلة الماضية، شكلت الأوبئة التي تسببها الفيروسات شديدة العدوى، مثل فيروس كورونا، وفيروس الحصبة، وفيروس نقص المناعة البشرية HIV، تهديدًا خطيرًا للصحة العامة. ومن منظور مجهري، تلعب العشوائية دورًا حاسمًا في عملية تكاثر الفيروسات، ومع ذلك، لا تزال الدراسات النظرية حول النماذج الوبائية التي تتضمن تأثيرات عشوائية بيولوجية معقولة محدودة. تهدف هذه الأطروحة إلى سد هذه الفجوة من خلال تحليل الديناميكيات التطورية للنماذج الوبائية العشوائية ودراسة تأثير الاضطرابات العشوائية على تطور الفيروسات وتطور الأمراض بشكل عام. في هذا العمل، نقوم بتطوير ودراسة نماذج عشوائية تدمج آليات إنتاج الفيروسات مع عمليات أورنشتاين-أولنبيك أو بلاك-كاراسينسكي. على وجه التحديد، نفترض أن بعض المعلمات الوبائية الأساسية، مثل معدل انتقال الخلايا من الطور الكامن إلى الطور المعدي، تتبع عملية أورنشتاين-أولنبيك. ضمن إطار رياضي محدد بدقة، نقوم بتطوير واعتماد مناهج تحليلية جديدة وغير تقليدية لإثبات الخصائص الأساسية لهذه النماذج العشوائية، بما في ذلك وجود وحيدة الحلول العالمية، ووجود توزيع ثابت، وتحديد الشروط اللازمة لانقراض المرض. بالإضافة إلى ذلك، نوضح أن إدخال الاضطرابات العشوائية بهذه الطريقة له مبررات رياضية قوية وأساس بيولوجي واضح. لدعم النتائج النظرية، يتم إجراء محاكاة رقمية في نهاية كل قسم، حيث تؤكد هذه المحاكاة صحة التحليل النظري وتوضح دقة الشروط والمعايير المستخلصة 2026-01-01T00:00:00Z https://dspace.univ-adrar.edu.dz/jspui/handle/123456789/9385 Title: Contribution of a bio-inspired meta-heuristic for optimization of localization in wireless sensor networks Authors: TABBI, AMINA; Rabhi, Seddik / Supervisor Abstract: Localization in Wireless Sensor Networks (WSNs) is a fundamental task that directly inf luences network accuracy and performance. Although many localization techniques have been proposed, several limitations remain, while bio-inspired optimization algorithms have shown strong effectiveness in this domain. In this work, two localization algorithms are proposed to improve the positioning of unknown nodes. The first, SLnO-CLA, combines the Centroid Localization Algorithm (CLA) with the Sea Lion Optimization (SLnO) algorithm. SLnO is used to optimize and refine the initial position estimate provided by CLA , improving localization accuracy, and accelerating the convergence. The second algorithm, referred to as IMP-SLnO, is an enhanced version of SLnO that focuses on improving stability and overall performance through multiple enhancement mechanisms that increase diversity, strengthen exploration, and speed up convergence. The performance of SLnO-CLA is evaluated and compared with the classical CLA algorithm across 30 independent runs using identical network deployments. Results show that SLnO-CLA reduces the Mean Localization Error (MLE) by 93.7% compared to plain CLA. The performance of IMP-SLnO is further evaluated against baseline SLnO and several well-known bio-inspired algorithms including Grey Wolf Optimization (GWO), Particle Swarm Optimization (PSO), Firefly Algorithm (FA), and SLnO-CLA. IMP-SLnO achieves an MLE of 0.2459 m, representing an 82.1% improvement over baseline SLnO, and outperforms all comparison algorithms across all reported metrics. 2026-01-01T00:00:00Z https://dspace.univ-adrar.edu.dz/jspui/handle/123456789/9384 Title: Anonymisation des données par apprentissage profonde(Data anonymization using deep learning) Authors: BOUDAOUD, Arbia; KABOU, SALHEDDINE / Supervisor Abstract: The increasing use of Electronic Health Records (EHRs) has created new opportunities for medical research and artificial intelligence, while raising significant concerns about patient privacy. Consequently, data anonymization has become essential for enabling secure data sharing without compromising the confidentiality of sensitive information. Traditional anonymization techniques, such as suppression, generalization, and differential privacy, often struggle to preserve the utility of complex longitudinal medical data. As an alternative, synthetic data generation has emerged as a promising anonymization approach, where artificial patient records are generated instead of releasing real ones, thereby preserving both privacy and data utility. Among deep learning methods, Generative Adversarial Networks (GANs) have shown great potential for synthetic medical data generation. However, existing GAN-based approaches suffer from two major limitations: mode collapse, which reduces the diversity of generated samples, and their black-box nature, which fails to explicitly model patients’ physiological states. To address these challenges, this thesis proposes a novel anonymization framework based on a Differentiable Hidden Markov Model (dHMM)- guided GAN. The proposed model combines explicit physiological state modeling with an LSTM-based patient history tracker to improve temporal consistency, while a MetropolisHastings-inspired latent space exploration strategy enhances sample diversity and mitigates mode collapse. Experimental results demonstrate that the proposed approach generates realistic, diverse, and clinically coherent synthetic medical records, providing an effective solution for privacy-preserving healthcare data sharing 2026-01-01T00:00:00Z