Fractional order cancer model infection in human with CD8+ T cells and anti-PD-L1 therapy: simulations and control strategy.

In order to comprehend the dynamics of disease propagation within a society, mathematical formulations are essential. The purpose of this work is to investigate the diagnosis and treatment of lung cancer in persons with weakened immune systems by introducing cytokines ( I L 2 & I L 12 ) and anti-PD-L1 inhibitors. To find the stable position of a recently built system TCD I L 2 I L 12 Z, a qualitative and quantitative analysis are taken under sensitive parameters. Reliable bounded findings are ensured by examining the generated system's boundedness, positivity, uniqueness, and local stability analysis, which are the crucial characteristics of epidemic models. The positive solutions with linear growth are shown to be verified by the global derivative, and the rate of impact across every sub-compartment is determined using Lipschitz criteria. Using Lyapunov functions with first derivative, the system's global stability is examined in order to evaluate the combined effects of cytokines and anti-PD-L1 inhibitors on people with weakened immune systems. Reliability is achieved by employing the Mittag-Leffler kernel in conjunction with a fractal-fractional operator because FFO provide continuous monitoring of lung cancer in multidimensional way. The symptomatic and asymptomatic effects of lung cancer sickness are investigated using simulations in order to validate the relationship between anti-PD-L1 inhibitors, cytokines, and the immune system. Also, identify the actual state of lung cancer control with early diagnosis and therapy by introducing cytokines and anti-PD-L1 inhibitors, which aid in the patients' production of anti-cancer cells. Investigating the transmission of illness and creating control methods based on our validated results will both benefit from this kind of research.

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.

Analysis and dynamical structure of glucose insulin glucagon system with Mittage-Leffler kernel for type I diabetes mellitus.

In this paper, we propose a fractional-order mathematical model to explain the role of glucagon in maintaining the glucose level in the human body by using a generalised form of a fractal fractional operator. The existence, boundedness, and positivity of the results are constructed by fixed point theory and the Lipschitz condition for the biological feasibility of the system. Also, global stability analysis with Lyapunov's first derivative functions is treated. Numerical simulations for fractional-order systems are derived with the help of Lagrange interpolation under the Mittage-Leffler kernel. Results are derived for normal and type 1 diabetes at different initial conditions, which support the theoretical observations. These results play an important role in the glucose-insulin-glucagon system in the sense of a closed-loop design, which is helpful for the development of artificial pancreas to control diabetes in society.

Mathematical study of polycystic ovarian syndrome disease including medication treatment mechanism for infertility in women.

Among women of reproductive age, PCOS (polycystic ovarian syndrome) is one of the most prevalent endocrine illnesses. In addition to decreasing female fertility, this condition raises the risk of cardiovascular disease, diabetes, dyslipidemia, obesity, psychiatric disorders and other illnesses. In this paper, we constructed a fractional order model for polycystic ovarian syndrome by using a novel approach with the memory effect of a fractional operator. The study population was divided into four groups for this reason: Women who are at risk for infertility, PCOS sufferers, infertile women receiving therapy (gonadotropin and clomiphene citrate), and improved infertile women. We derived the basic reproductive number, and by utilizing the Jacobian matrix and the Routh-Hurwitz stability criterion, it can be shown that the free and endemic equilibrium points are both locally stable. Using a two-step Lagrange polynomial, solutions were generated in the generalized form of the power law kernel in order to explore the influence of the fractional operator with numerical simulations, which shows the impact of the sickness on women due to the effect of different parameters involved.

Physiological and chaos effect on dynamics of neurological disorder with memory effect of fractional operator: A mathematical study.

BACKGROUND AND OBJECTIVE: To study the dynamical system, it is necessary to formulate the mathematical model to understand the dynamics of various diseases that are spread worldwide. The main objective of our work is to examine neurological disorders by early detection and treatment by taking asymptomatic. The central nervous system (CNS) is impacted by the prevalent neurological condition known as multiple sclerosis (MS), which can result in lesions that spread across time and place. It is widely acknowledged that multiple sclerosis (MS) is an unpredictable disease that can cause lifelong damage to the brain, spinal cord, and optic nerves. The use of integral operators and fractional order (FO) derivatives in mathematical models has become popular in the field of epidemiology. METHOD: The model consists of segments of healthy or barian brain cells, infected brain cells, and damaged brain cells as a result of immunological or viral effectors with novel fractal fractional operator in sight Mittag Leffler function. The stability analysis, positivity, boundedness, existence, and uniqueness are treated for a proposed model with novel fractional operators. RESULTS: Model is verified the local and global with the Lyapunov function. Chaos Control will use the regulate for linear responses approach to bring the system to stabilize according to its points of equilibrium so that solutions are bounded in the feasible domain. To ensure the existence and uniqueness of the solutions to the suggested model, it makes use of Banach's fixed point and the Leray Schauder nonlinear alternative theorem. For numerical simulation and results the steps Lagrange interpolation method at different fractional order values and the outcomes are compared with those obtained using the well-known FFM method. CONCLUSION: Overall, by offering a mathematical model that can be used to replicate and examine the behavior of disease models, this research advances our understanding of the course and recurrence of disease. Such type of investigation will be useful to investigate the spread of disease as well as helpful in developing control strategies from our justified outcomes.

Computational and stability analysis of Ebola virus epidemic model with piecewise hybrid fractional operator.

In this manuscript, we developed a nonlinear fractional order Ebola virus with a novel piecewise hybrid technique to observe the dynamical transmission having eight compartments. The existence and uniqueness of a solution of piecewise derivative is treated for a system with Arzel'a-Ascoli and Schauder conditions. We investigate the effects of classical and modified fractional calculus operators, specifically the classical Caputo piecewise operator, on the behavior of the model. A model shows that a completely continuous operator is uniformly continuous, and bounded according to the equilibrium points. The reproductive number R0 is derived for the biological feasibility of the model with sensitivity analysis with different parameters impact on the model. Sensitivity analysis is an essential tool for comprehending how various model parameters affect the spread of illness. Through a methodical manipulation of important parameters and an assessment of their impact on Ro, we are able to learn more about the resiliency and susceptibility of the model. Local stability is established with next Matignon method and global stability is conducted with the Lyapunov function for a feasible solution of the proposed model. In the end, a numerical solution is derived with Newton's polynomial technique for a piecewise Caputo operator through simulations of the compartments at various fractional orders by using real data. Our findings highlight the importance of fractional operators in enhancing the accuracy of the model in capturing the intricate dynamics of the disease. This research contributes to a deeper understanding of Ebola virus dynamics and provides valuable insights for improving disease modeling and public health strategies.

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.

Mathematical modeling and control of lung cancer with IL2 cytokine and anti-PD-L1 inhibitor effects for low immune individuals.

Mathematical formulations are crucial in understanding the dynamics of disease spread within a community. The aim of this work is to examine that the Lung Cancer detection and treatment by introducing IL2 and anti-PD-L1 inhibitor for low immune individuals. Mathematical model is developed with the created hypothesis to increase immune system by antibody cell's and Fractal-Fractional operator (FFO) is used to turn the model into a fractional order model. A newly developed system TCDIL2Z is examined both qualitatively and quantitatively in order to determine its stable position. The boundedness, positivity and uniqueness of the developed system are examined to ensure reliable bounded findings, which are essential properties of epidemic models. The global derivative is demonstrated to verify the positivity with linear growth and Lipschitz conditions are employed to identify the rate of effects in each sub-compartment. The system is investigated for global stability using Lyapunov first derivative functions to assess the overall impact of IL2 and anti-PD-L1 inhibitor for low immune individuals. Fractal fractional operator is used to derive reliable solution using Mittag-Leffler kernel. In fractal-fractional operators, fractal represents the dimensions of the spread of the disease and fractional represents the fractional ordered derivative operator. We use combine operators to see real behavior of spread as well as control of lung cancer with different dimensions and continuous monitoring. Simulations are conducted to observe the symptomatic and asymptomatic effects of Lung Cancer disease to verify the relationship of IL2, anti-PD-L1 inhibitor and immune system. Also identify the real situation of the control for lung cancer disease after detection and treatment by introducing IL2 cytokine and anti-PD-L1 inhibitor which helps to generate anti-cancer cells of the patients. Such type of investigation will be useful to investigate the spread of disease as well as helpful in developing control strategies from our justified outcomes.

Qualitative analysis and chaotic behavior of respiratory syncytial virus infection in human with fractional operator.

Respiratory syncytial virus (RSV) is the cause of lung infection, nose, throat, and breathing issues in a population of constant humans with super-spreading infected dynamics transmission in society. This research emphasizes on examining a sustainable fractional derivative-based approach to the dynamics of this infectious disease. We proposed a fractional order to establish a set of fractional differential equations (FDEs) for the time-fractional order RSV model. The equilibrium analysis confirmed the existence and uniqueness of our proposed model solution. Both sensitivity and qualitative analysis were employed to study the fractional order. We explored the Ulam-Hyres stability of the model through functional analysis theory. To study the influence of the fractional operator and illustrate the societal implications of RSV, we employed a two-step Lagrange polynomial represented in the generalized form of the Power-Law kernel. Also, the fractional order RSV model is demonstrated with chaotic behaviors which shows the trajectory path in a stable region of the compartments. Such a study will aid in the understanding of RSV behavior and the development of prevention strategies for those who are affected. Our numerical simulations show that fractional order dynamic modeling is an excellent and suitable mathematical modeling technique for creating and researching infectious disease models.

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.

Phytochemical, Geographical, and Pharmacological Retrospect of Genus Torilis.

BACKGROUND: Genus Torilis (Apiaceae) known as hedge parsley, encompasses 11-13 species distributed worldwide and shows potential pharmacological uses. Its phytochemical pattern is highly diversified including many phenolic and terpenic compounds. OBJECTIVE: This research-review provides new highlighting of structural organizations, structure-activity trends, taxonomical, tissue and geographical distribution of phytocompounds of Torilis genus from extensive statistical analyses of available data. METHODS: In extenso, exploration of documented literature and statistical data analyses were applied to update the phytochemical pool of the genus under several aspects including structural diversity, geographical distribution, biological compartmentations and pharmacological activities. RESULTS: Phytoconstituents were classified into homogeneous clusters that revealed to be associated with chemical constitutions (aglycone types, chemical groups) and distributions (through species, tissues, geographical). About bioactivities, terpenes were studied from a pharmacological point of view with relatively high frequencies for antifungal, antibacterial, cytotoxic and anti-inflammatory activities. Preliminary structure-activity relationships were highlighted implying opposite effects between hydroxylation and methylation in favor of different activities. Crude extracts and isolated compounds have shown several biological activities (antibacterial, anticancer, antiangiogenic, antiproliferative, etc.), thus providing authentic scientific proof for their diverse uses in folk medicines. CONCLUSION: The phytochemistry of the genus Torilis promises important perspectives in matters of pharmacological activities. These perspectives call for further investments in pharmacology because of (i) unbalance between phenolic and terpenic compounds according to the countries and (ii) more advanced current states of structural elucidations compared to biological evaluations.

Biological Evaluation and Computational Studies of Methoxy-flavones from Newly Isolated Radioresistant Micromonospora aurantiaca Strain TMC-15.

This study aims to determine UV-B resistance and to investigate computational analysis and antioxidant potential of methoxy-flavones of Micromonospora aurantiaca TMC-15 isolated from Thal Desert, Pakistan. The cellular extract was purified through solid-phase extraction and UV-Vis spectrum analysis indicated absorption peaks at λmax 250 nm, 343 nm, and 380 nm that revealed the presence of methoxy-flavones named eupatilin and 5-hydroxyauranetin. The flavones were evaluated for their antioxidant as well as protein and lipid peroxidation inhibition potential using di(phenyl)-(2,4,6-trinitrophenyl) iminoazanium (DPPH), 2,4-dinitrophenyl hydrazine (DNPH), and thiobarbituric acid reactive substances (TBARS) assays, respectively. The methoxy-flavones were further studied for their docking affinity and interaction dynamics to determine their structural and energetic properties at the atomic level. The antioxidant potential, protein, and lipid oxidation inhibition and DNA damage preventive abilities were correlated as predicted by computational analysis. The eupatilin and 5-hydroxyauranetin binding potential to their targeted proteins 1N8Q and 1OG5 is - 4.1 and - 7.5 kcal/mol, respectively. Moreover, the eupatiline and 5-hydroxyauranetin complexes illustrate van der Waals contacts and strong hydrogen bonds to their respective enzymes target. Both in vitro studies and computational analysis results revealed that methoxy-flavones of Micromonospora aurantiaca TMC-15 can be used against radiation-mediated oxidative damages due to its kosmotrophic nature. The demonstration of good antioxidant activities not only protect DNA but also protein and lipid oxidation and therefore could be a good candidate in radioprotective drugs and as sunscreen due to its kosmotropic nature.

Tumor micro-environment sensitive release of doxorubicin through chitosan based polymeric nanoparticles: An in-vitro study.

Conventional chemotherapy poses toxic effects to healthy tissues. A therapeutic system is thus required that can administer, distribute, metabolize, and excrete medicine from human body without damaging healthy cells. This is possible by designing a therapeutic system that can release drug at specific target tissue. In current work, novel chitosan (CS) based polymeric nanoparticles (PNPs) containing N-isopropyl acrylamide (NIPAAM) and 2-(di-isopropyl amino) ethyl methacrylate (DPA) are designed. The presence of available functional groups i.e. OH- (3262 cm-1), -NH2 (1542 cm-1), and CO (1642 cm-1), was confirmed by Fourier Transform Infra-red Spectrophotometry (FTIR). The surface morphology and average particle size (175 nm) was determined through Scanning Electron Microscope (SEM). X-Ray Diffractometry (XRD) studies confirmed the amorphous nature and excellent thermal stability of PNPs up to 100 °C with only 2.69% mass loss was confirmed by Thermogravimetric analysis (TGA). The pH sensitivity of such PNPs for release of encapsulated doxorubicin at malignant site was investigated. The encapsulation efficiency of PNPs was 89% (4.45 mg/5 mg) for doxorubicin (a chemotherapeutic) measured by using UV-Vis Spectrophotometer. The drug release profile of loaded PNPs was 88% (3.92 mg/4.45 mg) at pH 5.3, in 96 h. PNPs with varying DPA concentration can effectively be used to deliver chemotherapeutic agents with high efficacy.

Fractal-fractional operator for COVID-19 (Omicron) variant outbreak with analysis and modeling.

The fractal-fraction derivative is an advanced category of fractional derivative. It has several approaches to real-world issues. This work focus on the investigation of 2nd wave of Corona virus in India. We develop a time-fractional order COVID-19 model with effects of disease which consist system of fractional differential equations. Fractional order COVID-19 model is investigated with fractal-fractional technique. Also, the deterministic mathematical model for the Omicron effect is investigated with different fractional parameters. Fractional order system is analyzed qualitatively as well as verify sensitivity analysis. The existence and uniqueness of the fractional-order model are derived using fixed point theory. Also proved the bounded solution for new wave omicron. Solutions are derived to investigate the influence of fractional operator which shows the impact of the disease on society. Simulation has been made to understand the actual behavior of the OMICRON virus. Such kind of analysis will help to understand the behavior of the virus and for control strategies to overcome the disseise in community.

Analysis and Simulation of Fractional Order Smoking Epidemic Model.

In recent years, there are many new definitions that were proposed related to fractional derivatives, and with the help of these definitions, mathematical models were established to overcome the various real-life problems. The true purpose of the current work is to develop and analyze Atangana-Baleanu (AB) with Mittag-Leffler kernel and Atangana-Toufik method (ATM) of fractional derivative model for the Smoking epidemic. Qualitative analysis has been made to `verify the steady state. Stability analysis has been made using self-mapping and Banach space as well as fractional system is analyzed locally and globally by using first derivative of Lyapunov. Also derive a unique solution for fractional-order model which is a new approach for such type of biological models. A few numerical simulations are done by using the given method of fractional order to explain and support the theoretical results.

Analysis of COVID-19 epidemic model with sumudu transform.

In this paper, we develop a time-fractional order COVID-19 model with effects of disease during quarantine which consists of the system of fractional differential equations. Fractional order COVID-19 model is investigated with ABC technique using sumudu transform. Also, the deterministic mathematical model for the quarantine effect is investigated with different fractional parameters. The existence and uniqueness of the fractional-order model are derived using fixed point theory. The sumudu transform can keep the unity of the function, the parity of the function, and has many other properties that are more valuable. Solutions are derived to investigate the influence of fractional operator which shows the impact of the disease during quarantine on society.

Degradation of lignin by Bacillus altitudinis SL7 isolated from pulp and paper mill effluent.

Lignin is a major by-product of pulp and paper industries, and is resistant to depolymerization due to its heterogeneous structure. Degradation of lignin can be achieved by the use of potential lignin-degrading bacteria. The current study was designed to evaluate the degradation efficiency of newly isolated Bacillus altitudinis SL7 from pulp and paper mill effluent. The degradation efficiency of B. altitudinis SL7 was determined by color reduction, lignin content, and ligninolytic activity from degradation medium supplemented with alkali lignin (3 g/L). B. altitudinis SL7 reduced color and lignin content by 26 and 44%, respectively, on the 5th day of incubation, as evident from the maximum laccase activity. Optimum degradation was observed at 40 °C and pH 8.0. FT-IR spectroscopy and GC-MS analysis confirmed lignin degradation by emergence of the new peaks and identification of low-molecular-weight compounds in treated samples. The identified compounds such as vanillin, 2-methyoxyhenol, 3-methyl phenol, oxalic acid and ferulic acid suggested the degradation of coniferyl and sinapyl groups of lignin. Degradation efficiency of B. altitudinis SL7 towards high lignin concentration under alkaline pH indicated the potential application of this isolate in biological treatment of the lignin-containing effluents.

Generalized form of fractional order COVID-19 model with Mittag-Leffler kernel.

An important advantage of fractional derivatives is that we can formulate models describing much better systems with memory effects. Fractional operators with different memory are related to the different type of relaxation process of the nonlocal dynamical systems. Therefore, we investigate the COVID-19 model with the fractional derivatives in this paper. We apply very effective numerical methods to obtain the numerical results. We also use the Sumudu transform to get the solutions of the models. The Sumudu transform is able to keep the unit of the function, the parity of the function, and has many other properties that are more valuable. We present scientific results in the paper and also prove these results by effective numerical techniques which will be helpful to understand the outbreak of COVID-19.