A fractional-order model for optimizing combination therapy in heterogeneous lung cancer: integrating immunotherapy and targeted therapy to minimize side effects.

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.

Dynamical analysis of methicillin-resistant Staphylococcus aureus infection in North Cyprus with optimal control: prevalence and awareness.

The number of Methicillin-resistant Staphylococcus aureus (MRSA) cases in communities and hospitals is on the rise worldwide. In this work, a nonlinear deterministic model for the dynamics of MRSA infection in society was developed to visualize the significance of awareness in interventions that could be applied in the prevention of transmission with and without optimal control. Positivity and uniqueness were verified for the proposed corruption model to identify the level of resolution of infection factors in society. Furthermore, how various parameters affect the reproductive number R 0 and sensitivity analysis of the proposed model was explored through mathematical techniques and figures. The global stability of model equilibria analysis was established by using Lyapunov functions with the first derivative test. A total of seven years of data gathered from a private hospital consisting of inpatients and outpatients of MRSA were used in this model for numerical simulations and for observing the dynamics of infection by using a non-standard finite difference (NSFD) scheme. When optimal control was applied as a second model, it was determined that increasing awareness of hand hygiene and wearing a mask were the key controlling measures to prevent the spread of community-acquired MRSA (CA-MRSA) and hospital-acquired MRSA (HA-MRSA). Lastly, it was concluded that both CA-MRSA and HA-MRSA cases are on the rise in the community, and increasing awareness concerning transmission is extremely significant in preventing further spread.

A mathematical fractal-fractional model to control tuberculosis prevalence with sensitivity, stability, and simulation under feasible circumstances.

BACKGROUND: Tuberculosis, a global health concern, was anticipated to grow to 10.6 million new cases by 2021, with an increase in multidrug-resistant tuberculosis. Despite 1.6 million deaths in 2021, present treatments save millions of lives, and tuberculosis may overtake COVID-19 as the greatest cause of mortality. This study provides a six-compartmental deterministic model that employs a fractal-fractional operator with a power law kernel to investigate the impact of vaccination on tuberculosis dynamics in a population. METHODS: Some important characteristics, such as vaccination and infection rate, are considered. We first show that the suggested model has positive bounded solutions and a positive invariant area. We evaluate the equation for the most important threshold parameter, the basic reproduction number, and investigate the model's equilibria. We perform sensitivity analysis to determine the elements that influence tuberculosis dynamics. Fixed-point concepts show the presence and uniqueness of a solution to the suggested model. We use the two-step Newton polynomial technique to investigate the effect of the fractional operator on the generalized form of the power law kernel. RESULTS: The stability analysis of the fractal-fractional model has been confirmed for both Ulam-Hyers and generalized Ulam-Hyers types. Numerical simulations show the effects of different fractional order values on tuberculosis infection dynamics in society. According to numerical simulations, limiting contact with infected patients and enhancing vaccine efficacy can help reduce the tuberculosis burden. The fractal-fractional operator produces better results than the ordinary integer order in the sense of memory effect at diffract fractal and fractional order values. CONCLUSION: According to our findings, fractional modeling offers important insights into the dynamic behavior of tuberculosis disease, facilitating a more thorough comprehension of their epidemiology and possible means of control.

Flip bifurcation analysis and mathematical modeling of cholera disease by taking control measures.

To study the dynamical system, it is necessary to formulate the mathematical model to understand the dynamics of various diseases which are spread in the world wide. The objective of the research study is to assess the early diagnosis and treatment of cholera virus by implementing remedial methods with and without the use of drugs. A mathematical model is built with the hypothesis of strengthening the immune system, and a ABC operator is employed to turn the model into a fractional-order model. A newly developed system SEIBR, which is examined both qualitatively and quantitatively to determine its stable position as well as the verification of flip bifurcation has been made for developed system. The local stability of this model has been explored concerning limited observations, a fundamental aspect of epidemic models. We have derived the reproductive number using next generation method, denoted as " R 0 ", to analyze its impact rate across various sub-compartments, which serves as a critical determinant of its community-wide transmission rate. The sensitivity analysis has been verified according to its each parameters to identify that how much rate of change of parameters are sensitive. Atangana-Toufik scheme is employed to find the solution for the developed system using different fractional values which is advanced tool for reliable bounded solution. Also the error analysis has been made for developed scheme. Simulations have been made to see the real behavior and effects of cholera disease with early detection and treatment by implementing remedial methods without the use of drugs in the community. Also identify the real situation the spread of cholera disease after implementing remedial methods with and without the use of drugs. Such type of investigation will be useful to investigate the spread of virus as well as helpful in developing control strategies from our justified outcomes.

A generalized Chebyshev operational method for Volterra integro-partial differential equations with weakly singular kernels.

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.

Fractional order model of MRSA bacterial infection with real data fitting: Computational Analysis and Modeling.

Bacterial infections in the health-care sector and social environments have been linked to the Methicillin-Resistant Staphylococcus aureus (MRSA) infection, a type of bacteria that has remained an international health risk since the 1960s. From mild colonization to a deadly invasive disease with an elevated mortality rate, the illness can present in many different forms. A fractional-order dynamic model of MRSA infection developed using real data for computational and modeling analysis on the north side of Cyprus is presented in this paper. Initially, we tested that the suggested model had a positively invariant region, bounded solutions, and uniqueness for the biological feasibility of the model. We study the equilibria of the model and assess the expression for the most significant threshold parameter, called the basic reproduction number (ℛ0). The reproductive number's parameters are also subjected to sensitivity analysis through mathematical methods and simulations. Additionally, utilizing the power law kernel and the fixed-point approach, the existence, uniqueness, and generalized Ulam-Hyers-Rassias stability are presented. Chaos Control was used to regulate the linear responses approach to bring the system to stabilize according to its points of equilibrium, taking into account a fractional-order system with a managed design where solutions are bound in the feasible domain. Finally, numerical simulations demonstrating the effects of different parameters on MRSA infection are used to investigate the impact of the fractional operator on the generalized form of the power law kernel through a two-step Newton polynomial method. The impact of fractional orders is emphasized in the study so that the numerical solutions support the importance of these orders on MRSA infection. With the application of fractional order, the significance of cognizant antibiotic usage for MRSA infection is verified.

Within-host delay differential model for SARS-CoV-2 kinetics with saturated antiviral responses.

The present study discussed a model to describe the SARS-CoV-2 viral kinetics in the presence of saturated antiviral responses. A discrete-time delay was introduced due to the time required for uninfected epithelial cells to activate a suitable antiviral response by generating immune cytokines and chemokines. We examined the system's stability at each equilibrium point. A threshold value was obtained for which the system switched from stability to instability via a Hopf bifurcation. The length of the time delay has been computed, for which the system has preserved its stability. Numerical results show that the system was stable for the faster antiviral responses of epithelial cells to the virus concentration, i.e., quick antiviral responses stabilized patients' bodies by neutralizing the virus. However, if the antiviral response of epithelial cells to the virus increased, the system became unstable, and the virus occupied the whole body, which caused patients' deaths.

Generalized Ulam-Hyers-Rassias stability and novel sustainable techniques for dynamical analysis of global warming impact on ecosystem.

Marine structure changes as a result of climate change, with potential biological implications for human societies and marine ecosystems. These changes include changes in temperatures, flow, discrimination, nutritional inputs, oxygen availability, and acidification of the ocean. In this study, a fractional-order model is constructed using the Caputo fractional operator, which singular and nol-local kernel. A model examines the effects of accelerating global warming on aquatic ecosystems while taking into account variables that change over time, such as the environment and organisms. The positively invariant area also demonstrates positive, bounded solutions of the model treated. The equilibrium states for the occurrence and extinction of fish populations are derived for a feasible solution of the system. We also used fixed-point theorems to analyze the existence and uniqueness of the model. The generalized Ulam-Hyers-Rassias function is used to analyze the stability of the system. To study the impact of the fractional operator through computational simulations, results are generated employing a two-step Lagrange polynomial in the generalized version for the power law kernel and also compared the results with an exponential law and Mittag Leffler kernel. We also produce graphs of the model at various fractional derivative orders to illustrate the important influence that the fractional order has on the different classes of the model with the memory effects of the fractional operator. To help with the oversight of fisheries, this research builds mathematical connections between the natural world and aquatic ecosystems.

A fractional-order mathematical model for lung cancer incorporating integrated therapeutic approaches.

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 [Formula: see text] is 2.6, indicating that a lung cancer cell would generate 2.6 new cancer cells during its lifetime. The reproduction coefficient [Formula: see text] 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 [Formula: see text] (the rate of division of cancer stem cells) and [Formula: see text] (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.

A Novel Multistep Iterative Technique for Models in Medical Sciences with Complex Dynamics.

This paper proposes a three-step iterative technique for solving nonlinear equations from medical science. We designed the proposed technique by blending the well-known Newton's method with an existing two-step technique. The method needs only five evaluations per iteration: three for the given function and two for its first derivatives. As a result, the novel approach converges faster than many existing techniques. We investigated several models of applied medical science in both scalar and vector versions, including population growth, blood rheology, and neurophysiology. Finally, some complex-valued polynomials are shown as polynomiographs to visualize the convergence zones.

Crank-Nicholson difference scheme for the system of nonlinear parabolic equations observing epidemic models with general nonlinear incidence rate.

In this work, we study second order Crank-Nicholson difference scheme (DS) for the approximate solution of problem (1). The existence and uniqueness of the theorem on a bounded solution of Crank-Nicholson DS uniformly with respect to time step τ is proved. In practice, theoretical results are presented on four systems of nonlinear parabolic equations to explain how it works on one and multidimensional problems. Numerical results are provided.

Investigation of skin self-examination and sunscreen use in adolescents in northern Cyprus.

INTRODUCTION: Regular skin self-examination (SSE) is very important for the early diagnosis of malignant melanoma (MM). Since sun exposure is the most important trigger factor for the development of skin cancers, effective and regular sun protection is the main preventive method. AIM: To investigate the awareness of SSE, risky nevus and sun protection of the adolescents in the Turkish Republic of Northern Cyprus (TRNC). MATERIAL AND METHODS: The data used within this research were obtained from questionnaires administered to volunteer high school students in the TRNC. RESULTS: 39.8% of the participants included in the study stated that they conducted SSE. All the participants who said they conducted SSE reported that they performed a face exam. The body regions that the participants did not examine were the scalp (47.7%), foot (36.9%), back (35.4%) and genital area (35.4%). The features of the nevus perceived by the participants as risk factors included rapid growth, bleeding and itching. While 74% of respondents said they used sunscreen products, only 9% of users reported using them every day. CONCLUSIONS: In the TRNC where the exposure to the sun is high, young people perform skin examinations at high rates in order to monitor their nevi. Nevertheless, the results of this research show that hard-to-reach areas are neglected.

Stability analysis of fractional order model on corona transmission dynamics.

In this paper a fractional order mathematical model is constructed to study the dynamics of corona virus in Oman. The model consists of a system of eight non-linear fractional order differential equations in Caputo sense. Existence and uniqueness as well as the stability analysis of the solution of the model are given. The stability analysis is in the frame of Ulam-Hyers and generalized Ulam-Hyers criteria. Numerical simulations are given to support the theoretical results. Many informations on the dynamics of COVID -19 in Oman were obtained using this model. Also many informations on the qualitative behaviour of the model were obtained.

In Vitro Comparison of Fluoride, Magnesium, and Calcium Phosphate Materials on Prevention of White Spot Lesions around Orthodontic Brackets.

One common negative side effect of orthodontic treatment with fixed appliances is the development of white spot lesions (WSLs) around brackets. This study is aimed at comparing the efficacy of various oral hygiene practices in preventing enamel demineralization around orthodontic brackets under similar in vitro conditions. The study included 90 extracted bovine incisors, which were randomized into six groups: fluoride toothpaste (FT), nonfluoride toothpaste (NFT), fluoride varnish plus fluoride toothpaste (FV+FT), CPP-ACP varnish plus fluoride toothpaste (CPP-ACP+FT), medical minerals gel plus nonfluoride toothpaste (MMG+NFT), and no intervention (control). All groups were subjected to demineralization and remineralization cycles. Visual appraisals were used to evaluate the changes in the enamel surface appearance at the beginning and end of the experiment. The changes in the demineralization degree were evaluated by measuring the Ca+2 concentration in the demineralization solution at different time points. The majority of teeth in the CPP-ACP+FT group exhibited no shift in appearance, whereas in the other groups, a slight change in enamel translucency was observed. At all the time points, the Ca+2 concentration in the demineralization solution in the CPP-ACP+FT group was the least among all other groups. At day 5, MMG+NFT's preventive efficacy was significantly higher than FV+FT's, but at days 10, 15, and 19, their efficacy was similar. However, at all the time points, MMG+NFT's efficacy was significantly higher than that of control, whereas FV+FT's efficacy was decreased at days 10, 15, and 19 and was close to the efficacy of control. To fight WSLs, early diagnosis was of great importance and examination of the tooth surface after air-drying for 5 s was recommended.

Dynamics of HIV/AIDS in Turkey from 1985 to 2016.

In this paper, we formulated a mathematical model that studies the dynamics of HIV/AIDS in Turkey from 1985 to 2016. We find two equilibrium points, disease free equilibrium and endemic equilibrium. Global stability analysis of the equilibria was conducted using Lyapunov function which depends on the basic reproduction ratio R 0. If R 0 < 1, the disease free equilibrium point is globally asymptotically stable, and if R 0 ≥ 1 the endemic equilibrium point is globally asymptotically stable. We computed and predicted the basic reproduction ratios across all the years. It was found out that there were flaws in the exact values of R 0 which is related to the poor registration system of HIV/AIDS in Turkey. Hence, there is need for the government to improve the system in order to cover the actual cases of the disease. The increase of the basic reproduction ratio over the years also shows the need for the relevant authorities to adopt appropriate control measures in combating the disease.

Dynamics of Immune Checkpoints, Immune System, and BCG in the Treatment of Superficial Bladder Cancer.

This paper aims to study the dynamics of immune suppressors/checkpoints, immune system, and BCG in the treatment of superficial bladder cancer. Programmed cell death protein-1 (PD-1), cytotoxic T-lymphocyte-associated antigen 4 (CTLA4), and transforming growth factor-beta (TGF-ß) are some of the examples of immune suppressors/checkpoints. They are responsible for deactivating the immune system and enhancing immunological tolerance. Moreover, they categorically downregulate and suppress the immune system by preventing and blocking the activation of T-cells, which in turn decreases autoimmunity and enhances self-tolerance. In cancer immunotherapy, the immune checkpoints/suppressors prevent and block the immune cells from attacking, spreading, and killing the cancer cells, which leads to cancer growth and development. We formulate a mathematical model that studies three possible dynamics of the treatment and establish the effects of the immune checkpoints on the immune system and the treatment at large. Although the effect cannot be seen explicitly in the analysis of the model, we show it by numerical simulations.

Morphometric analysis of the infraorbital foramen, canal and groove using cone beam CT: considerations for creating artificial organs.

PURPOSE: The aim of this study was to examine the anatomy and variations of the infraorbital foramen and its surroundings via morphometric measurements using cone beam computed tomography (CBCT) scans derived from a 3D volumetric rendering program. METHODS: 354 sides of CBCT scans from 177 patients were examined in this study. DICOM data from these images were exported to Maxilim® software in order to generate 3D surface models. The morphometric measurements were done for infraorbital foramen (IOF), infraorbital groove (IOG) and infraorbital canal (IOC). All images were evaluated by 1 radiologist. To assess intra-observer reliability, the Wilcoxon matched-pairs signed rank test was used. Differences between sex, side, age and measurements were evaluated using chi-square and paired t-test and measurements were evaluated using 1-way ANOVA tests. Differences were considered significant when p<0.05. RESULTS: The most common shape was oval for IOF and parallel for IOC without any accessory foramen. The results showed that females have smaller dimensions for the measurements between the two foramen rotundum (FR), FR-IOF, sella-FR, center of the IOF (cIOF)-nasion (N), cIOF-NB (nasion-B) (p>0.05). No significant difference was found according to age groups (p>0.05). CONCLUSIONS: These results provide detailed knowledge of the anatomical characteristics in this particular area. CBCT imaging with lower radiation dose and thin slices can be a powerful tool for anesthesia procedures like infra orbital nerve blocks, for surgical approaches like osteotomies and neurectomies and also for generating artificial prostheses.

Knowledge, attitudes and behaviour towards sexually transmitted diseases in Turkish Cypriot adolescents.

BACKGROUND: The incidence of sexually transmitted diseases (STDs) is increasing among adolescents all around the world. There may be differences in knowledge and attitudes among different cultures and ethnic populations. The aim of this study is to determine knowledge, attitudes and behaviour of Turkish Cypriot adolescents related to STDs. OBJECTIVES: To assess knowledge of STDs, attitudes towards sexual behaviour and STDs among the secondary school students. METHODS: A cross sectional study, with a sample size of 423 students, was conducted by using a semi-structured questionnaire. Simple random sampling method was applied during the selection of the sample. RESULTS: The mean age of all participants was 15.61 +/- 1.22, 211 (49.88%) of them were male and 212 (50.12%) female. The majority of students (91.25%) stated that they had some knowledge about STDs; hovewer, 8.75% of the participants did not have any knowledge at all. Most of them, 42.32% described school as a source of information on STDs, nonetheless, only 7.57% of the group cited health care professionals as the information source. The majority of students (97.64%) has never been treated for STDs. Among 423 applicants, 93.14% indicated that they would have appreciated information about STDs during the high school years. CONCLUSIONS: There is a general understanding that the students are willing to participate and are in need of seminars that will be held about STDs during high school attendance. Furthermore, awareness raising educational events on this matter should be reviewed and revised in order to come up with more powerful ways of fighting against STDs transmission in this young population group of Turkish Cypriot (TC) community.

Effect of isotretinoin on prothrombin time (PT), international normalized ratio (INR), and activated partial thromboplastin time (aPTT).

Patients with severe acne may need elective/urgent surgical interventions during treatment with isotretinoin and it is critical for the surgeon to consider the possible effects of this medication on coagulation systems. The aim of this study is to determine the changes in prothrombin time (PT), international normalized ratio (INR), and activated partial thromboplastin time (aPTT) during isotretinoin treatment. PT, aPTT, and INR values of 51 severe acne patients were evaluated during routine pre-treatment biochemical analysis. Only patients with normal values were included in the study. The results of before and after 1 month treatment were compared statistically. There were no statistically significant change in mean alanine aminotranferease (ALT), aspartate aminotransferase (AST), PT, and INR values after treatment. A significant increase in aPTT was detected. The INR values, which are more trusted and safe, showed no difference. Isotretinoin seems to have no effect on these coagulation parameters.

Mathematical models for human cancer incidence rates: application to results from Europe, including North Cyprus.

The overall cancer incidence rate declines at very old age. Possible causes of this decline include the effects of cross-sectional data that transform cohort dynamics into age patterns, population heterogeneity that selects individuals susceptible to cancer, a decline in some carcinogenic exposure in older individuals, underdiagnosis, and the effects of individual aging that slow down major physiological processes in an organism. Here several mathematical models contributing to the explanation of this phenomenon are discussed, with extension of the Strehler and Mildvan model of aging and mortality to the analysis of data on cancer incidence at old age (data source: International Agency for Research on Cancer). The model can help explain the observed time trends and age patterns of cancer incidence rates.