ABSTRACT
Recently, the area devoted to fractional calculus has given much attention by researchers. The reason behind such huge attention is the significant applications of the mentioned area in various disciplines. Different problems of real world processes have been investigated by using the concepts of fractional calculus and important and applicable outcomes were obtained. Because, there has been a lot of interest in fractional differential equations. It is brought on by both the extensive development of fractional calculus theory and its applications. The use of linear and quadratic perturbations of nonlinear differential equations in mathematical models of a variety of real-world problems has received a lot of interest. Therefore, motivated by the mentioned importance, this research work is devoted to analyze in detailed, a class of fractal hybrid fractional differential equation under Atangana- Baleanu- Caputo ABC derivative. The qualitative theory of the problem is examined by using tools of non-linear functional analysis. The Ulam-Hyer's (U-H) type stability criteria is also applied to the consider problem. Further, the numerical solution of the model is developed by using powerful numerical technique. Lastly, the Wazewska-Czyzewska and Lasota Model, a well-known biological model, verifies the results. Several graphical representations by using different fractals fractional orders values are presented. The detailed discussion and explanations are given at the end.
Subject(s)
Fractals , Models, Biological , Algorithms , Nonlinear DynamicsABSTRACT
Measles, a highly contagious viral disease, spreads primarily through respiratory droplets and can result in severe complications, often proving fatal, especially in children. In this article, we propose an algorithm to solve a system of fractional nonlinear equations that model the measles disease. We employ a fractional approach by using the Caputo operator and validate the model's by applying the Schauder and Banach fixed-point theory. The fractional derivatives, which constitute an essential part of the model can be treated precisely by using the Broyden and Haar wavelet collocation methods (HWCM). Furthermore, we evaluate the system's stability by implementing the Ulam-Hyers approach. The model takes into account multiple factors that influence virus transmission, and the HWCM offers an effective and precise solution for understanding insights into transmission dynamics through the use of fractional derivatives. We present the graphical results, which offer a comprehensive and invaluable perspective on how various parameters and fractional orders influence the behaviours of these compartments within the model. The study emphasizes the importance of modern techniques in understanding measles outbreaks, suggesting the methodology's applicability to various mathematical models. Simulations conducted by using MATLAB R2022a software demonstrate practical implementation, with the potential for extension to higher degrees with minor modifications. The simulation's findings clearly show the efficiency of the proposed approach and its application to further extend the field of mathematical modelling for infectious illnesses.
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Colorectal cancer is among the well-known forms of cancer and a prominent cause of cancer demises worldwide. In vitro experiments reinforced by animal studies, as well as epidemiological studies of human colorectal cancer propose that the growth of this disease can be moderated by eating aspects. Dietary intake including green vegetables and fruits may result in the reduction of colon cancer chances. The finding suggests that the combinations of dietary nutrients may deliver additive or synergistic effects and might be a powerful method to avoid or eradicate colon cancer beginning and/or development. Flavonols are one of the most widespread dietary nutrients of the polyphenols-flavonoids and major constituent of Allium and Brassicaceae vegetables. Flavonols present in vegetables of Allium and Brassicaceae family are kaempferol, myricetin, quercetin, and isorhamnetin. These flavonols are claimed to have antiproliferative activity in vivo and in vitro against colorectal cancer. The objective of this review is to summarize the role of flavonols obtained from dietary sources in the prevention and treatment of colorectal cancer.
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Similarity measures and distance measures are used in a variety of domains, such as data clustering, image processing, retrieval of information, and recognizing patterns, in order to measure the degree of similarity or divergence between elements or datasets. p , q - quasirung orthopair fuzzy ( p , q - QOF) sets are a novel improvement in fuzzy set theory that aims to properly manage data uncertainties. Unfortunately, there is a lack of research on similarity and distance measure between p , q - QOF sets. In this paper, we investigate different cosine similarity and distance measures between to p , q - quasirung orthopair fuzzy sets ( p , q - ROFSs). Firstly, the cosine similarity measure and the Euclidean distance measure for p , q - QOFSs are defined, followed by an exploration of their respective properties. Given that the cosine measure does not satisfy the similarity measure axiom, a method is presented for constructing alternative similarity measures for p , q - QOFSs. The structure is based on the suggested cosine similarity and Euclidean distance measures, which ensure adherence to the similarity measure axiom. Furthermore, we develop a cosine distance measure for p , q - QOFSs that connects similarity and distance measurements. We then apply this technique to decision-making, taking into account both geometric and algebraic perspectives. Finally, we present a practical example that demonstrates the proposed justification and efficacy of the proposed method, and we conclude with a comparison to existing approaches.
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This paper demonstrates, a numerical method to solve the one and two dimensional Burgers' equation involving time fractional Atangana-Baleanu Caputo ( ABC ) derivative with a non-singular kernel. The numerical stratagem consists of a quadrature rule for time fractional ( ABC ) derivative along with Haar wavelet (HW) approximations of one and two dimensional problems. The key feature of the scheme is to reduce fractional problems to the set of linear equations via collocation procedure. Solving the system gives the approximate solution of the given problem. To verify the effectiveness of the developed method five numerical examples are considered. Besides this, the obtained simulations are compared with some published work and identified that proposed technique is better. Moreover, computationally the convergence rate in spatiotemporal directions is presented which shows order two convergence. The stability of the proposed scheme is also described via Lax-Richtmyer criterion. From simulations it is obvious that the scheme is quite useful for the time fractional problems.
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Biosimilars are biological drugs created from living organisms or that contain living components. They share an identical amino-acid sequence and immunogenicity. These drugs are considered to be cost-effective and are utilized in the treatment of cancer and other endocrine disorders. The primary aim of biosimilars is to predict biosimilarity, efficacy, and treatment costs; they are approved by the Food and Drug Administration (FDA) and have no clinical implications. They involve analytical studies to understand the similarities and dissimilarities. A biosimilar manufacturer sets up FDA-approved reference products to evaluate biosimilarity. The contribution of next-generation sequencing is evolving to study the organ tumor and its progression with its impactful therapeutic approach on cancer patients to showcase and target rare mutations. The study shall help to understand the future perspectives of biosimilars for use in gastro-entero-logic diseases, colorectal cancer, and thyroid cancer. They also help target specific organs with essential mutational categories and drug prototypes in clinical practices with blood and liquid biopsy, cell treatment, gene therapy, recombinant therapeutic proteins, and personalized medications. Biosimilar derivatives such as monoclonal antibodies like trastuzumab and rituximab are common drugs used in cancer therapy. Escherichia coli produces more than six antibodies or antibody-derived proteins to treat cancer such as filgrastim, epoetin alfa, and so on.
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Hepatitis B virus (HBV) infection is a global public health issue. We offer a comprehensive analysis of the dynamics of HBV, which can be successfully controlled with vaccine and treatment. Hepatitis B virus (HBV) causes a significantly more severe and protracted disease compared to hepatitis A. While it initially presents as an acute disease, in approximately 5 to 10% of cases, it can develop into a chronic disease that causes permanent damage to the liver. The hepatitis B virus can remain active outside the body for at least seven days. If the virus penetrates an individual's body without immunization, it may still result in infection. Upon exposure to HBV, the symptoms often last for a duration ranging from 10 days to 6 months. In this study, we developed a new model for Hepatitis B Virus (HBV) that includes asymptomatic carriers, vaccination, and treatment classes to gain a comprehensive knowledge of HBV dynamics. The basic reproduction number [Formula: see text] is calculated to identify future recurrence. The local and global stabilities of the proposed model are evaluated for values of [Formula: see text] that are both below and above 1. The Lyapunov function is employed to ensure the global stability of the HBV model. Further, the existence and uniqueness of the proposed model are demonstrated. To look at the solution of the proposed model graphically, we used a useful numerical strategy, such as the non-standard finite difference method, to obtain more thorough numerical findings for the parameters that have a significant impact on disease elimination. In addition, the study of treatment class in the population, we may assess the effectiveness of alternative medicines to treat infected populations can be determined. Numerical simulations and graphical representations are employed to illustrate the implications of our theoretical conclusions.
Subject(s)
Computer Simulation , Hepatitis B virus , Hepatitis B , Humans , Hepatitis B/epidemiology , Hepatitis B/prevention & control , Hepatitis B virus/physiology , Epidemics/prevention & control , Hepatitis B Vaccines/therapeutic use , Hepatitis B Vaccines/administration & dosage , Basic Reproduction Number , VaccinationABSTRACT
The prevalence of Alzheimer's disease and other forms of dementia is increasing worldwide, and finding effective treatments for these conditions is a major public health challenge. Natural bioactive drugs have been identified as a promising source of potential treatments, due to their ability to target multiple pathways and their low toxicity. This paper reviews the current state of research on natural bioactive drugs used in the treatment of Alzheimer's disease and other dementias. The paper summarizes the findings of studies on various natural compounds, including curcumin, resveratrol, caffeine, genistein, quercetin, GinkoBiloba, Withaniasomnifera, Ginseng Brahmi, Giloy, and huperzine, and their effects on cognitive function, neuroinflammation, and amyloid-beta accumulation. In this review, we discuss the mechanism of action involved in the treatment of Alzheimer's disease. The paper also discusses the challenges associated with developing natural bioactive drugs for dementia treatment, including issues related to bioavailability and standardization. Finally, the paper suggests directions for future research in this area, including the need for more rigorous clinical trials and the development of novel delivery systems to improve the efficacy of natural bioactive drugs. Overall, this review highlights the potential of natural bioactive drugs as a promising avenue for the development of safe and effective treatments for Alzheimer's disease and other dementias.
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In this manuscript, we present a novel concept known as the fuzzy Sehgal contraction, specifically designed for self-mappings defined in the context of a fuzzy metric space. Our primary objective is to explore the existence and uniqueness of fixed points for self-mappings in fuzzy metric space. To support our conclusions, we present a detailed illustrative case that demonstrates the superiority of the convergence obtained with our suggested method to those currently recorded in the literature. Moreover, we provide graphical depictions of the convergence behavior, which makes our study more understandable and transparent. Additionally, we extend the application of our results to address the existence and uniqueness of solutions for Volterra integral equations.
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Fuzzy Logic , Algorithms , Models, TheoreticalABSTRACT
AIM: The present work is focus on development of anti-psoriasis activity of Karanjin (isolated from Pongamia pinnata seed oil) loaded liposome based lotion for enhancement of skin permeation and retention. METHOD: Karanjin was isolated using liquid-liquid extraction method and characterised by HPLC analysis and partition coefficient. Further, isolated Karanjin was loaded into liposomes using thin-film hydration technique and optimised by Box-Behnken design. Selected optimised batch was characterised their mean diameter, PDI, zeta potential, and entrapment efficiency, morphology (by TEM), FTIR and ex-vivo skin retention. Additionally, Karanjin loaded liposomes were formulated into lotion and characterise their rheological, spreadability, texture, ex-vivo skin permeation & retention, stability and anti-psoriatic activity in mouse tail model. RESULT: The yield of Karanjin from seed oil was 0.1% w/v and have lipophilic nature. The optimised liposomal formulation showed 195 ± 1.8 nm mean diameter, 0.271 ± 0.02 PDI, -27.0 ± 2.1 mV zeta potential and 61.97 ± 2.5% EE. TEM image revel the spherical shap of liposome surrounded by single phospholipid bilayer and no interection between drug and excipients. Further, lotion was prepared by 0.1% w/v carbopol and found to 615 mPa.sec viscosity, good thixotropic behaviour, spreadability and texture. There was 22.44% increase in drug permeation for Karanjin loaded liposomal lotion compared to pure Karanjin lotion, confirm by ex-vivo permeation and retention. While, in-vivo study revel the liposomal lotion of Karanjin was found to have 16.09% higher drug activity then 5% w/w conventional Karanjin lotion. CONCLUSION: Karanjin loaded liposomal lotion have an effective anti-psoriatic agent and showed better skin permeation and retention than the conventional Karanjin lotion.
Subject(s)
Liposomes , Psoriasis , Skin Absorption , Animals , Mice , Psoriasis/drug therapy , Disease Models, Animal , Administration, Cutaneous , Skin , MaleABSTRACT
This paper deals with the mathematical analysis of Tuberculosis by using fractal fractional operator. Mycobacterium TB is the bacteria that causes tuberculosis. This airborne illness mostly impacts the lungs but may extend to other body organs. When the infected individual coughs, sneezes or speaks, the bacterium gets released into the air and travels from one person to another. Five classes have been formulated to study the dynamics of this disease: susceptible class, infected of DS, infected of MDR, isolated class, and recovered class. To study the suggested fractal fractional model's wellposedness associated with existence results, and boundedness of solutions. Further, the invariant region of the considered model, positive solutions, equilibrium point, and reproduction number. One would typically employ a fractional calculus approach to obtain numerical solutions for the fractional order Tuberculosis model using the Adams-Bashforth-Moulton method. The fractional order derivatives in the model can be approximated using appropriate numerical schemes designed for fractional order differential equations.
Subject(s)
Fractals , Mycobacterium tuberculosis , Tuberculosis , Humans , Tuberculosis/microbiology , Mycobacterium tuberculosis/pathogenicity , Models, Theoretical , Models, Biological , AlgorithmsABSTRACT
This research conducts a detailed analysis of a nonlinear mathematical model representing COVID-19, incorporating both environmental factors and social distancing measures. It thoroughly analyzes the model's equilibrium points, computes the basic reproductive rate, and evaluates the stability of the model at disease-free and endemic equilibrium states, both locally and globally. Additionally, sensitivity analysis is carried out. The study develops a sophisticated stability theory, primarily focusing on the characteristics of the Volterra-Lyapunov (V-L) matrices method. To understand the dynamic behavior of COVID-19, numerical simulations are essential. For this purpose, the study employs a robust numerical technique known as the non-standard finite difference (NSFD) method, introduced by Mickens. Various results are visually presented through graphical representations across different parameter values to illustrate the impact of environmental factors and social distancing measures.
Subject(s)
COVID-19 , Nonlinear Dynamics , Physical Distancing , SARS-CoV-2 , COVID-19/epidemiology , COVID-19/prevention & control , Humans , SARS-CoV-2/isolation & purification , Models, Theoretical , EnvironmentABSTRACT
The Phyllanthus genus is very important plant traded as a raw herbal medicine in India. Commonly known as 'Bhumyamalaki' (Phyllanthus species) has been used for the prevention and treatment of jaundice. Phyllanthus is rich in diversity of bioactive compounds such as lignans, alkaloids, terpenoids, flavonoids, and tannins. Among some metabolites such as phyllanthin, hypophyllanthin, 8, 9-epoxy brevifolin, brevifolin, quercetin, gallic acid, elagic acid, and brevifolin carboxylate have been shown to have hepatoprotective and antioxidant activity found in this genus. The basic objective of this review was to overview the hepatoprotective activity based on the other available data from various plants of the Phyllanthus species including Phyllanthus amarus, Phyllanhtus urinaria, Phyllanthus fraternus, Phyllanthus maderaspatenis, Phyllanthus simplex, Phyllanthus emblica, Phyllanthus debillis, Phyllanthus tenellus, Phyllanthus polyphyllus, Phyllanthus reticulates, Phyllanthus indofischerii, Phyllanthus acidus, Phyllanthus niruri, Phyllanthus rheedii, Phyllanthus kozhikodianus, and Phyllanthus longiflorus. These species studied had considerable hepatoprotective potential. The secondary data, each in vitro and in vivo studies confirm the capacity of Phyllanthus species used as a remedy for jaundice or liver disease in addition to having antioxidants. Furthermore, it could be concluded that herbal drugs have the least side effects and are taken into considered safe for human health, they are able to substantially alternative synthetic drugs in the future.
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Pythagorean cubic fuzzy sets represent an advancement beyond conventional interval-valued Pythagorean sets, integrating the principles of Pythagorean fuzzy sets and interval-valued Pythagorean fuzzy sets. Given the critical significance of distance measures in real-world decision-making and pattern recognition tasks, it is noteworthy that there exists a notable gap in the literature regarding distance measures specifically tailored for Pythagorean cubic fuzzy sets. The objectives of this paper are:â¢To define novel generalized distance measures between Pythagorean cubic fuzzy sets (PCFSs) to tackle intricate decision-making challenges.â¢These novel distance measures are undergoing testing on a real-world scenario concerning the management of anxiety and depression to evaluate their effectiveness and practical application.â¢We have illustrated the boundedness and nonlinear characteristics inherent in these distance measures. In addition, we conduct comparative analyses with existing approaches to validate the proposed methodology, thereby providing insights into its advantages and potential applications.
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Background: There are no large studies examining survival in patients receiving haemodialysis in India or considering centre-level effects on survival. We measured survival variation between dialysis centres across India and evaluated the extent to which differences are explained by measured centre characteristics. Methods: This is a multilevel analysis of patient survival in centres of the NephroPlus dialysis network consisting of 193 centres across India. Patients receiving haemodialysis at a centre for ≥90 days between April 2014 and June 2019 were included, with analyses restricted to centres with ≥10 such patients. The primary outcome was all-cause mortality, measured from 90 days after joining a centre. Proportional hazards models with shared frailty were used to model centre- and patient-level effects on survival. Findings: Amongst 23,601 patients (median age 53 years; 29% female), the unadjusted centre-specific 180-day Kaplan-Meier survival estimates ranged between 55% (95% confidence interval [CI] 38-80%) and 100%, with a median of 88% (interquartile interval 83%-92%). After accounting for multilevel factors, estimated 180-day survival ranged between 83% (73-89%) and 97% (95-98%), with 90% 180-day survival in the average centre. The mortality rate in patients attending rural centres was 32% (Hazard Ratio 1.32; 95% CI 1.06-1.65) higher than those at urban centres in adjusted analyses. Multiple patient characteristics were associated with mortality. Interpretation: This is the first national benchmark for survival amongst dialysis patients in India. Centre- and patient-level characteristics are associated with survival but there remains unexplained variation between centres. As India continues to widen dialysis access, ongoing quality improvement programs will be an important part of ensuring that patients experience the best possible outcomes at the point of care. Funding: This project received no external funding.
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One of the most important organic compounds, also known as a Schiff base, imine, or azomethine, has been associated with several biological processes. The group is a component of both natural or synthetic chemicals and functions as both a precursor and an intermediary in the synthesis of therapeutically active substances. The review highlights the various non-metal Schiff bases' structure-activity relationship (SAR) studies, general model, docking, and design approach for anticonvulsant actions. Schiff bases serve as linkers in numerous synthetic compounds with a variety of activities, according to the findings of several investigations. As a result, the current review will give readers a thorough understanding of the key ideas put forth by different researchers regarding the anticonvulsant properties of Schiff bases. It will serve as a valuable information source for those planning to synthesize new anticonvulsant molecules that contain Schiff bases as pharmacophores or biologically active moieties.
Subject(s)
Anticonvulsants , Schiff Bases , Schiff Bases/chemistry , Schiff Bases/pharmacology , Schiff Bases/chemical synthesis , Anticonvulsants/chemistry , Anticonvulsants/pharmacology , Anticonvulsants/chemical synthesis , Humans , Structure-Activity Relationship , Animals , Molecular StructureABSTRACT
The research article in hand provides a new mechanism that deals with the investigation of the triangular analytical fuzzy solutions (TAFS) of the two-dimensional fuzzy fractional order wave equation (2-D FFWE) through the Hukuhara conformable fractional derivative (HCFD) along with the concept of [gH] and [gH-p] differentiability. The mechanism consists of a fuzzy traveling wave method coupled with additive operating splitting (AOS). The procedure for the aforesaid mechanism starts with the extension of the HCFD to the fuzzy conformable fractional derivative (FCFD). Furthermore, some properties of FCFD that play a vital role in this study like, ([i-gH],[ii-gH],[i-p],[ii-p])-differentiability, switching point, fuzzy chain rule, and traveling wave method are discussed in detail. Further, fuzzy traveling wave method coupled with the procedure of the additive operating splitting (AOS) method is adopted to investigate the triangular analytical fuzzy solution of the Two-dimensional fuzzy wave equation (2-D FWE). Finally, some examples are provided that support our arguments.
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Human beings possess trillions of microbial cells in a symbiotic relationship. This relationship benefits both partners for a long time. The gut microbiota helps in many bodily functions from harvesting energy from digested food to strengthening biochemical barriers of the gut and intestine. But the changes in microbiota composition and bacteria that can enter the gastrointestinal tract can cause infection. Several approaches like culture-independent techniques such as high-throughput and meta-omics projects targeting 16S ribosomal RNA (rRNA) sequencing are popular methods to investigate the composition of the human gastrointestinal tract microbiota and taxonomically characterizing microbial communities. The microbiota conformation and diversity should be provided by whole-genome shotgun metagenomic sequencing of site-specific community DNA associating genome mapping, gene inventory, and metabolic remodelling and reformation, to ease the functional study of human microbiota. Preliminary examination of the therapeutic potency for dysbiosis-associated diseases permits investigation of pharmacokinetic-pharmacodynamic changes in microbial communities for escalation of treatment and dosage plan. Gut microbiome study is an integration of metagenomics which has influenced the field in the last two decades. And the incorporation of artificial intelligence and deep learning through "omics-based" methods and microfluidic evaluation enhanced the capability of identification of thousands of microbes.
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Deep Learning , Gastrointestinal Microbiome , Microbiota , Humans , Artificial Intelligence , Microbiota/genetics , Machine LearningABSTRACT
OBJECTIVE: Suicide disproportionately affects low- and middle-income countries and evidence regarding prevention approaches developed in high income countries may not be applicable in these settings. We conducted an umbrella review to assess whether the conclusions of suicide prevention systematic reviews accurately reflect the studies contained within those reviews in terms of setting generalizability. METHODS: We conducted database searches in PubMed/Medline, Embase, PsycInfo, PsychExtra, OVID global health, and LILACS/BECS. We included systematic reviews with the outcome of suicide, including bereavement studies where suicide death was also the exposure. RESULTS: Out of the 147 reviews assessed, we found that over 80% of systematic reviews on suicide deaths do not provide an accurate summary of review findings with relation to geographic relevance and ultimately generalizability. CONCLUSION: Systematic reviews are often the resource used by practitioners and policymakers to guide services. Misleading reviews can detrimentally impact suicide prevention efforts in LMICs. We call for systematic reviewers to be responsible when generalizing the findings of their reviews particularly in the abstracts.
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Since there is a clear correlation between poverty and corruption, mathematicians have been actively researching the concept of poverty and corruption in order to develop the optimal strategy of corruption control. This work aims to develop a mathematical model for the dynamics of poverty and corruption. First, we study and analyze the indicators of corruption and poverty rates by applying the linear model along with the Eviews program during the study period. Then, we present a prediction of poverty rates for 2023 and 2024 using the results of the standard problem-free model. Next, we formulate the model in the frame of Caputo fractional derivatives. Fundamental properties, including equilibrium points, basic reproduction number, and positive solutions of the considered model are obtained using nonlinear analysis. Sufficient conditions for the existence and uniqueness of solutions are studied via using fixed point theory. Numerical analysis is performed by using modified Euler method. Moreover, results about Ulam-Hyers stability are also presented. The aforementioned results are presented graphically. In addition, a comparison with real data and simulated results is also given. Finally, we conclude the work by providing a brief conclusion.