Glioblastoma Multiforme (GBM) is a highly aggressive and lethal form of brain tumor, presenting significant challenges in treatment and management. This study proposes an advanced control model for the management of GBM, focusing on the optimization of drug therapies and adaptive regulation of tumor volume. Leveraging fractional-order mathematical modeling, the approach integrates mathematical modeling techniques with control theory to develop comprehensive strategies for GBM management. It introduces a novel fractional-order mathematical model that uniquely integrates nutrient dynamics and blood flow into the analysis of Glioblastoma Multiforme (GBM) progression. By combining fractional-order calculus with adaptive PID control, the approach provides a more accurate representation of tumor behavior and enables personalized, real-time treatment optimization. The proposed control models aim to optimize drug therapies by dynamically adjusting treatment parameters based on real-time tumor volume monitoring. This adaptive approach allows for personalized treatment regimens tailored to the specific characteristics of the tumor, enhancing therapeutic efficacy while minimizing adverse effects. The proposed framework advances current methodologies by addressing memory effects and long-range dependencies in tumor growth, offering new insights for precision medicine. By harnessing the capabilities of fractional-order modeling, our research provides a novel framework for advancing the management of GBM, offering new insights and strategies for combating this formidable disease.

This paper presents a Respiratory Syncytial Virus (RSV) epidemic model for a continuous human population of super-spreading infected individuals. The model uses a generalized fractal-fractional derivative with the Mittag-Leffler function to analyze transmission, considering different infection stages, and demonstrates the effectiveness of certain individuals as viral spreaders. Using linear growth and Lipschitz requirements, the study determines the existence, uniqueness, positiveness, and boundedness of a proposed fractional-order system in order to assess its viability. The global stability of equilibrium points is verified by the Lyapunov function, and the effects of the model's parameters are investigated through sensitivity analysis. To comprehend the model's behavior and create preventative measures for infected people, a numerical simulation of its activity is also carried out. By offering a more realistic depiction of virus behavior at various dimensions and population effects, the fractal-fractional model enhances comprehension and forecasts. The results highlight the importance of fractional order and its fitting function in the model by demonstrating how input parameters affect the dynamic behavior of RSV infection. Such an investigation will aid in understanding the behavior of the RSV and develop prevention measures for infected individuals.

This study explores the impact of the Leadership in Energy and Environmental Design (LEED) certification system on healthcare services in private hospitals in North Cyprus using a fractional-order system of equations. The Near East Hospital (NEH) earned Gold-level certification with 79 points, while Burhan Nalbanto & gbreve;lu Hospital (BNH) obtained 31 points. Through sensitivity analysis of indoor air quality and sustainable land criteria, the study demonstrates that hospitals adopting LEED certification provide superior service quality. The findings suggest that government hospitals could benefit from aligning with green certification criteria, potentially improving patient outcomes. Data collected from NEH and BNH support a positive relationship between green certification and increased patient and employee satisfaction, with significant evidence $ (p \lt 0.05) $ (p<0.05) distinguishing LEED-certified hospitals from non-certified ones. The study also evaluates how hospital expansions affect the applicability of certification programs and the management of COVID-19, focusing on criteria such as sustainable sites, water efficiency, and indoor environmental quality. The analysis provides insights for healthcare administrators and policymakers seeking to enhance hospital infrastructure to meet certification standards, improve healthcare services, and better manage future pandemics. The research underscores the importance of green certification in improving patient care, employee satisfaction, and overall hospital performance.

In this paper, we developed a mathematical model for pancreatic cancer progression using a system of nonlinear partial differential equations (PDEs) with time delays, capturing disease dynamics in the human body. The model represents six key cell populations involved in pancreatic cancer: cancer cells (), pancreatic stellate cells (), stromal cells (), extracellular matrix- degrading enzymes (), tumor-associated macrophages (), and immunosuppressive cells (). For biological feasibility, we established model existence and uniqueness via the method of continuity and Banach's contraction principle, with global stability verified through the Lyapunov method. Sensitivity analysis identified critical factors such as cancer cell division, stromal cell activation, and immune cell infiltration, as targets for effective treatment. Optimal control and PID strategies demonstrated potential in limiting cancer proliferation and reprogramming the tumor microenvironment, while simulations highlighted the need for timely and sustained interventions. The results emphasize the importance of early surgery and immunomodulation in maximizing treatment efficacy, offering new insights into personalized and adaptive approaches to improve patient outcomes in pancreatic cancer treatment.

Pseudomonas aeruginosa, a resilient gram-negative bacterium, poses a persistent threat as a leading cause of nosocomial infections, particularly in resource-constrained regions. Despite existing treatment and control measures, the bacterium continues to challenge healthcare systems, especially in developing nations. This paper introduces a fractional-order model to elucidate the dynamic behavior of nosocomial infections caused by P. aeruginosa and to compare the efficacy of carbapenems and aminoglycosides in treatment. The model’s existence and uniqueness are established, and both global and local stability are confirmed. The effective reproduction number is computed, revealing an epidemic potential with a value of 1.02 in Northern Cyprus. Utilizing real-life data from a university hospital and employing numerical simulations, our results indicate that patients exhibit higher sensitivity and lower resistance to aminoglycoside treatment compared to carbapenems. Aminoglycosides consistently outperform carbapenems across key metrics, including the reduction of susceptible population, infection numbers, treatment efficacy, total infected population, hospital occupancy, and effective reproduction number. The fractional-order approach emerges as a suitable and insightful tool for studying the transmission dynamics of the disease and assessing treatment effectiveness. This research provides a robust foundation for refining treatment strategies against P. aeruginosa infections, contributing valuable insights for healthcare practitioners and policymakers alike.

This research paper focused on the solution of systems of fractional integro-differential equations (FIDEs) of the Volterra type with variable coefficients. The proposed approach combined the tau method and shifted Gegenbauer polynomials in a matrix form. The investigation of the existence and uniqueness of solutions for these systems was carried out using Krasnoselskii's fixed point theorem. The equations employed Caputo-style derivative operators, and to minimize computational operations involving derivatives and multiplications, integral and product operational matrices were derived. By introducing suitable polynomial approximations and employing the tau spectral method, the original system of FIDE was transformed into an algebraic system. Solving this algebraic system provided approximate solutions to the main system. Error bounds were computed in the Gegenbauer-weighted Sobolev space. The proposed algorithm was implemented and tested on two systems of integro-fractional differential equations to demonstrate its efficiency and simplicity. By varying the parameter $ \sigma $ in the Gegenbauer polynomials, the impact of this variation on the approximate solutions can be observed. A comparison with another method utilizing the block-by-block approach was also presented.

Abstract. Ayo VI, Adondua MA, Morayo AE, Ekele JU, Amilo D, Ochuele DA, Ayantse LM, Barrah C, Abdulsalam IO, Eya SB, Iheanacho CC, Tibile ST, Mohammed RI, Barde CE. 2023. Effect of Lactuca sativa supplemented diet on Poloxamer 407 induced hyperlipidemic albino rats (Rattus norvegicus). Asian J Nat Prod Biochem 21: 67-78. Cardiovascular diseases (CVDs) have primarily contributed to the global disease burden. They represent the leading cause of mortality and healthcare expenditures in developed and third-world nations, responsible for approximately 30 percent of global deaths and 10 percent of global diseases annually. This study investigated the effects of a Lactuca sativa L. (lettuce) supplemented diet on Poloxamer 407-induced hyperlipidemic albino rats. Twenty-four (24) rats were grouped into six groups of treatments, i.e., four rats in each treatment. Treatments applied in this study were: control treatment (feed and water only), a P-407 induced without Atorvastatin, a P-407 induced treated with Atorvastatin, and P-407 induced with 10%, 30%, and 50% L. sativa supplemented diet. P407 was administered intraperitoneally at 1000 mg/kg body weight. Body weight was measured every three days for 14 days. Blood sample collection was carried out for the analysis of lipid profiles (High-Density Lipoprotein Cholesterol (HDL-C), Low-Density Lipoprotein Cholesterol (LDL-C), Very Low-Density Lipoprotein (VLDL), Triacylglycerides (TAG), and Total Cholesterol (TC)) and liver function parameters (ALP, ALT, AST, GGT, TP, ALB and GLB). The liver and brain tissues were analyzed for lipid peroxidation levels. Results showed that induction of P407 resulted in a higher body weight gain (p<0.05) compared to other treatments. The treatment groups other than the P-407 treatment showed a significant decrease in Total Cholesterol (TC), triacylglycerides (TAG), and LDL cholesterol levels and a significant increase in HDL cholesterol. The TC, TAG, LDL-C, and HDL-C levels in treating P-407 with a 50% L. sativa-supplemented diet did not differ (P>0.05) compared to the control treatment. The atherogenic risk prediction indices indicated a decreased risk in the treated groups with Atorvastatin or L. sativa-supplemented diet. Furthermore, liver function parameters were better in the treatment groups with Atorvastatin or L. sativa-supplemented diet, including decreased liver function parameters and increased total protein, albumin, and globulin levels. The L. sativa-supplemented diet also exhibited anti-lipid peroxidation activity, as indicated by reduced malondialdehyde (MDA) levels. In conclusion, the L. sativa-supplemented diet had hypolipidemic effects, anti-lipid peroxidation activity, and hepatoprotective effects, suggesting its potential as an antihyperlipidemic agent.

Volterra integro-partial differential equations with weakly singular kernels (VIPDEWSK) are utilized to model diverse physical phenomena. A matrix collocation method is proposed for determining the approximate solution of this functional equation category. The method employs shifted Chebyshev polynomials of the fifth kind (SCPFK) to construct two-dimensional pseudo-operational matrices of integration, avoiding the need for explicit integration and thereby speeding up computations. Error bounds are examined in a Chebyshev-weighted space, providing insights into approximation accuracy. The approach is applied to several experimental examples, and the results are compared with those obtained using the Bernoulli wavelets and Legendre wavelets methods.

This research presents a novel approach to address the complexities of heterogeneous lung cancer dynamics through the development of a Fractional-Order Model. Focusing on the optimization of combination therapy, the model integrates immunotherapy and targeted therapy with the specific aim of minimizing side effects. Notably, our approach incorporates a clever fusion of Proportional-Integral-Derivative (PID) feedback controls alongside the optimization process. Unlike previous studies, our model incorporates essential equations accounting for the interaction between regular and mutated cancer cells, delineates the dynamics between immune cells and mutated cancer cells, enhances immune cell cytotoxic activity, and elucidates the influence of genetic mutations on the spread of cancer cells. This refined model offers a comprehensive understanding of lung cancer progression, providing a valuable tool for the development of personalized and effective treatment strategies. the findings underscore the potential of the optimized treatment strategy in achieving key therapeutic goals, including primary tumor control, metastasis limitation, immune response enhancement, and controlled genetic mutations. The dynamic and adaptive nature of the treatment approach, coupled with economic considerations and memory effects, positions the research at the forefront of advancing precision and personalized cancer therapeutics.

The utilization of time-fractional Burgers' equations is widespread, employed in modeling various phenomena such as heat conduction, acoustic wave propagation, gas turbulence, and the propagation of chaos in nonlinear Markov processes. This study introduces a novel pseudo-operational collocation method, leveraging two-variable Jacobi polynomials. These polynomials are obtained through the Kronecker product of their one- variable counterparts, concerning both spatial (x) x ) and temporal (t) t ) domains. The study explores the impact of four parameters (0, 0, 9, a, & ccedil; > -1) ) on the accuracy of resulting approximate solutions, marking the first examination of such influence. Collocation nodes in a tensor approach are constructed employing the roots of one-variable Jacobi polynomials of varying degrees in x and t . The study delves into analyzing how the distribution of these roots affects the outcomes. Consequently, pseudo-operational matrices are devised to integrate both integer and fractional orders, presenting a novel methodological advancement. By employing these matrices and appropriate approximations, the governing equations transform into an algebraic system, facilitating computational analysis. Furthermore, the existence and uniqueness of the equations under study are investigated and the study estimates error bounds within a Jacobi-weighted space for the obtained approximate solutions. Numerical simulations underscore the simplicity, applicability, and efficiency of the proposed matrix spectral scheme.

This study presents an enhanced fractional-order mathematical model for analyzing the dynamics of Klebsiella pneumonia infections and antibiotic resistance over time. The model incorporates fractional Caputo derivative operators and kernel, to provide a more comprehensive understanding of the complex temporal dynamics. The model consists of three groups: Susceptible (S), Infected (I), and Resistant (R) individuals, each controlled by a fractional differential equation. The model represents the interaction between infection, recovery from infection, and the possible development of antibiotic resistance in susceptible individuals. The existence, uniqueness, stability, and alignment of the model’s prediction to the observed data were analyzed and buttressed with numerical simulations. The results show that imipenem has the highest efficacy compared with ertapenem and meropenem category drugs. The estimated reproduction number and reproduction coefficient illustrate the potential impact of this model in improving treatment strategies, while the memory effects highlight the advantages of fractional differentiation. The model predicts an increased possibility of antibiotic resistance despite effective treatment, suggesting a new treatment approach.

This study examines diabetes risk in women through predictive machine learning models and fractional- order physiological modeling. Machine learning models, including Bagged Trees, k-Nearest Neighbors (k-NN), Decision Trees, SVM (Support Vector Machine), and Logistic Regression, were applied to assess accuracy in diabetes prediction. Bagged Trees achieved the highest performance, with over 99% accuracy across metrics, and a user-friendly GUI-enabled real-time risk assessment. The GUI interface designed for these models provided users with accessible, dynamic feedback, enhancing usability for real-time assessment. Analysis revealed notable correlations, including age with pregnancies (0.54) and BMI with skin thickness (0.39), suggesting key factors in diabetes risk. Findings show that Glucose, BMI, Blood Pressure, and Diabetes Pedigree Function emerge as the top influential features, across all models. Using fractional-order modeling, we simulated glucose, insulin, BMI, and blood pressure changes over time, showing that higher fractional orders aligned with increased response dynamics. Together, these methods offer a comprehensive view of diabetes risk factors in women. By combining machine learning’s predictive power with the detailed, time-sensitive insights of fractional-order modeling, this study highlights key risk indicators and deepens our understanding of diabetes dynamics, ultimately supporting more effective risk assessment and management strategies. This dual approach provides an enriched perspective on diabetes risk factors and offers improved strategies for prediction and management.

Colorectal cancer (CRC) poses a significant global public health challenge as its prevalence continues to increase. This study delves into the intricate dynamics of metastatic CRC by utilizing a novel fractional-order model. Through a comprehensive analysis of existing literature and clinical data, we introduce an innovative fractional-order model tailored to metastatic CRC. This model encapsulates key factors like tumor growth, immune response, and therapeutic interventions. Our findings underscore the crucial role of epithelial cells (E) within the tumor microenvironment, emphasizing their significance due to their high sensitivity. Additionally, the influence of adenomatous polyps (P) is noteworthy, given their potential to transform into cancerous entities. Remarkably, the concentration of inflammatory cells (C) significantly impacts the model, shedding light on the pivotal role of the immune response. We implement a clever fusion of feedback control and Proportional–Integral–Derivative (PID) controllers, enabling dynamic self-adjustment and precision. Our results indicate that achieving high efficacy in treating metastatic colorectal cancer necessitates a synergistic and simultaneous application of immunotherapy and surgery. Also, surgical intervention should exert a slightly higher intensity than immunotherapy, even when administered concurrently. The PID control strategy offers a promising method for fine-tuning concentrations over time. These investigations enable a thorough exploration of how fractional-order parameters influence tumor progression, interactions with the immune system, and treatment outcomes. We conduct sensitivity analysis to pinpoint crucial model parameters governing the system’s dynamic behavior. The insights gleaned from our study hold significant promise for advancing treatment protocols and personalized medicine tailored to CRC patients.

Abstract 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.

This study proposes a nabla discrete fractional-order system of differential equations to model lung cancer and its interactions with lung epithelial cells, mutated cells, oncogenes, tumor suppressor genes, immune cells, cytokines, growth factors, angiogenic factors, and extracellular matrix. The proposed model can help predict cancer growth, metastasis, and response to treatment. Analytical results show the system is stable with a unique solution, and the model predicts that the immune system responds to cancer cells but eventually becomes overpowered. The numerical analysis employed the forward and backward Euler method and demonstrated that changes in parameter values have significant effects on the steady-state solution. The findings show that the growth of lung epithelial cells or their interaction with immune cells can cause an increase in the number of lung cancer cells. Conversely, an increase in cell death or a reduction in the interaction between lung epithelial cells and immune cells can decrease the number of lung cancer cells. The study highlights the usefulness of the nabla discrete fractional model in studying lung cancer dynamics.

This paper addresses the dynamics of lung cancer by employing a fractional-order mathematical model that investigates the combined therapy of surgery and immunotherapy. The significance of this study lies in its exploration of the effects of surgery and immunotherapy on tumor growth rate and the immune response to cancer cells. To optimize the treatment dosage based on tumor response, a feedback control system is designed using control theory, and Pontryagin’s Maximum Principle is utilized to derive the necessary conditions for optimality. The results reveal that the reproduction number $$(R_0)$$ is 2.6, indicating that a lung cancer cell would generate 2.6 new cancer cells during its lifetime. The reproduction coefficient $$(R_c)$$ is 0.22, signifying that cancer cells divide at a rate that is 0.22 times that of normal cells. The simulations demonstrate that the combined therapy approach yields significantly improved patient outcomes compared to either treatment alone. Furthermore, the analysis highlights the sensitivity of the steady-state solution to variations in $$k_5$$ (the rate of division of cancer stem cells) and $$k_{13}$$ (the rate of differentiation of cancer stem cells into progenitor cells). This research offers clinicians a valuable tool for developing personalized treatment plans for lung cancer patients, incorporating individual patient factors and tumor characteristics. The novelty of this work lies in its integration of surgery, immunotherapy, and control theory, extending beyond previous efforts in the literature.

COVID-19 has been an outbreak since December 2019 all around the world. There exist many studies in literature that examines the future of the pandemic and the effect of control strategies via mathematical modeling. Main aim of mathematical modeling in epidemiology and health sciences is applying the theory to real world health problems. In this paper, world population is divided into four compartments for the construction of SVIR model. That is, it is assumed that population consists of susceptible (S), vaccinated (V), infected (I), and recovered (R) individuals. Fractional mathematical models are very popular nowadays since it counts previous state of problems. While the construction of this model, fractional derivative is added with the purpose of seeing memory effect.