Bilgen Kaymakamzade

The transmission mechanisms of most infectious diseases are generally well understood from an epidemiological standpoint. To mathematically and quantitatively characterize the spread of these diseases, various classical epidemic models-such as the SIR, SIS, SEIR, and SIRS frameworks-have been formulated and thoroughly investigated. In the present paper, the initial value problem for the system of semilinear parabolic differential equations arising in epidemic models with a general semilinear incidence rate in a Hilbert space with a self-adjoint positive definite operator is investigated. The main theorem on the existence and uniqueness of bounded solutions for this system is established. In applications, theorems on the existence and uniqueness of bounded solutions for two types of systems of semilinear partial differential equations arising in epidemic models are proved. A first-order accurate finite difference scheme is developed to construct approximate solutions for this system. We further prove a theorem that guarantees the existence and uniqueness of bounded solutions for the discrete problem, independently of the time step. The theoretical results are supported by applications, where bounded solutions of the continuous system and their corresponding discrete approximations are demonstrated. Finally, numerical results are presented to illustrate the effectiveness and accuracy of the proposed scheme.

The study aims to identify the factors influencing In Vitro Fertilization (IVF) outcomes at Near East University (NEU) hospital in Northern Cyprus, by linking the different IVF model compartments and using mathematical modeling to simulate the dynamics of the procedure. The proposed model has five compartments, and when compared to classical integer-order models, the fractional-order model under the Caputo sense used in this model provides a more accurate representation of biological mechanisms by accounting for the impact of memory and complicated connections that affect IVF outcomes. The surface plots of each variable illustrates how this variable changes over time at fractional order [ ], indicating stronger memory effects and modeling real life situations. This research shows the simulation of each variable at different fractional-order values and population and how the fractional orders significantly influence the interaction between compartments. The framework’s local and global stability has been achieved, and the uniqueness of its solutions is investigated. The model highlights the significance of clinical strategy optimization, including sperm concentration, egg retention, embryo survival, and transplantation success. This model bridges the gap between mathematical analysis and reproductive health care, facilitating further investigations and clinical utilization. Positive beta Human Chorionic Gonadotropin (bHCG) and live birth based on complete cycles are key indicators of IVF success, reflecting modern clinical practice and promoting safe behavior, which can guide patient counseling and influence public policy.

This research develops a mathematical model to explore the complex dynamics linking healthcare, environmental sustainability, and Sustainable Development Goals (SDGs). Using fractional calculus with Caputo derivatives, the model captures the intertwined nature of these systems. It analyzes relationships among health status, healthcare economics, public awareness, and SDG progress over time, offering a comprehensive framework for these global challenges. Through detailed simulations, the study reveals dynamic feedback loops and time-dependent effects, highlighting system complexity. Calibrating fractional order parameters clarifies each variable's influence, enhancing understanding of overall dynamics. The results provide valuable insights for policymakers and researchers, supporting efforts toward a healthier, sustainable future. This work advances mathematical modeling in interdisciplinary fields and lays a foundation for future studies addressing global sustainability challenges.

Travel-associated cystitis is a growing health concern, marked by increased UTI rates among travelers. Uropathogenic E. coli and other Enterobacterales are the primary pathogens, often resistant to commonly used antibiotics. Treatments include trimethoprim, trimethoprim/sulfamethoxazole, β-lactams, fluoroquinolones, nitrofurantoin, and fosfomycin tromethamine, selected for efficacy and pharmacokinetics. Rational antimicrobial use is vital to limit antimicrobial resistance (AMR). Evidence-based treatment aligned with resistance patterns is essential. Mathematical modeling provides a useful tool to simulate resistance trends and assess therapies. This study evaluates key antibiotics in managing travel-associated cystitis and highlights modeling's role in AMR control. Susceptibility data for ciprofloxacin, trimethoprim/sulfamethoxazole, and nitrofurantoin were analyzed in recent local travelers and foreign tourists in Northern Cyprus. Observed differences in susceptibility support revising empirical treatment to improve outcomes and prevent resistant strain spread.

In this paper, a [ ]-dimensional generalized Sawada–Kotera (2D-gSK) equation, with significant applications in quantum gravity field theory, is explored. The study begins by bilinearizing the 2D-gSK equation using the Bell polynomial (BP) method and continues by finding its multiple solitons, after verifying integrability properties, through the simplified Hirota method. Some theorems regarding the existence of multi-lump waves are formally presented as direct results of multiple solitons. To complete the studies, some other specific nonlinear waves of the 2D-gSK equation, such as breather, complexiton, and Jacobi waves, are constructed in a detailed manner. In the end, as a result of the multidimensional and density representations, the dynamic features of such nonlinear waves are assessed. This work provides valuable results regarding nonlinear waves of the 2D-gSK equation and their dynamics.

This study compares the views of mathematics teachers in private and public schools on mathematics education during the COVID-19 pandemic from their perspectives after the pandemic, focusing on factors influencing secondary and high school mathematics education. In this study, the survey method was used to collect data. The survey method was employed to obtain information for this investigation. During the 2023–2024 school year, 644 math teachers took part in the study. Of these, 260 were from private schools, and 384 were from public schools. There are 10,323 teachers in public schools and 694 in private schools, and this sample size is more than the 371 participants that are needed for statistical purposes (based on Cochran’s formula at a 95% confidence level and a 5% margin of error). A scale consisting of thirteen 5-point Likert-type questions was developed by researchers for data collection, and mathematical modeling techniques were employed. Factor analysis using SPSS 24.00 revealed four key factors influencing teachers’ responses: teachers’ professional development and support, job satisfaction, students’ engagement, and teaching experience. The results highlight significant disparities between public and private schools in mathematics education, attributed to various factors to be elucidated further in the subsequent discussion.

This study examines how the implementation of the Leadership in Energy and Environmental Design (LEED)certification system has affected healthcare services in private hospitals in North Cyprus. The Near EastUniversity (NEU) hospital achieved Gold-level recognition with a minimum score of 79 points, while Dr.Burhan Nalbanto ̆glu Hospital (BNH) received 31 points. Through sensitivity analysis of indoor air qualityand sustainable land criteria, it becomes evident that hospitals adopting LEED certification systems offerhigher-quality services and present distinct advantages. The findings suggest that aligning government hos-pitals with green certification criteria may contribute to improved patient outcomes. Furthermore, datacollected from government hospitals and the Near East Hospital support a positive relationship betweengreen hospital criteria and enhanced patient and employee satisfaction. Statistical analysis reveals signifi-cant evidence (p < 0.05) that distinguishes hospitals meeting the green hospital certification criteria fromthose that do not. The study also examined the effects of hospital expansions on the applicability of per-formance certificate programs and the management of COVID-19. Various criteria, including LEED points,sustainable sites, regional priorities, water efficiency, design innovation, materials and resources, and indoorenvironmental quality, are analyzed using data from two hospitals, YD ̈U and BNH, to assess changes inthese criteria before and after the expansions. The results provide valuable insights for decision-makers andhealthcare administrators seeking to enhance hospital infrastructure and operations to meet certificationstandards and ensure effective pandemic management. This study highlights the importance of adoptinggreen certification criteria in hospital infrastructure and management to enhance patient outcomes, employeesatisfaction, and overall service quality.