Investigation and application of a classical piecewise hybrid with a fractional derivative for the epidemic model: Dynamical transmission and modeling.

In this research, we developed an epidemic model with a combination of Atangana-Baleanu Caputo derivative and classical operators for the hybrid operator's memory effects, allowing us to observe the dynamics and treatment effects at different time phases of syphilis infection caused by sex. The developed model properties, which take into account linear growth and Lipschitz requirements relating the rate of effects within its many sub-compartments according to the equilibrium points, include positivity, unique solution, exitance, and boundedness in the feasible domain. After conducting sensitivity analysis with various parameters influencing the model for the piecewise fractional operator, the reproductive number R0 for the biological viability of the model is determined. Generalized Ulam-Hyers stability results are employed to preserve global stability. The investigated model thus has a unique solution in the specified subinterval in light of the Banach conclusion, and contraction as a consequence holds for the Atangana-Baleanu Caputo derivative with classical operators. The piecewise model that has been suggested has a maximum of one solution. For numerical solutions, piecewise fractional hybrid operators at various fractional order values are solved using the Newton polynomial interpolation method. A comparison is also made between Caputo operator and the piecewise derivative proposed operator. This work improves our knowledge of the dynamics of syphilis and offers a solid framework for assessing the effectiveness of interventions for planning and making decisions to manage the illness.

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.

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.

Study of Kinetics and the Working Mechanism of Silica-Coated Amino-Functionalized CoFe2O4 Ferrite Nanoparticles to Treat Wastewater for Heavy Metals.

This study used a simple coprecipitation method to produce pristine, silica-coated, and amino-functionalized CoFe2O4 nanoadsorbents. Amino-functionalization was done to increase the active surface area and metal ion removal efficiency. Both pristine and functionalized adsorbents were employed to recover Pb(II), Zn(II), and Cu(II) ions from wastewater. The adsorption tests were performed by varying the initial concentration of metal ions and contact time at a fixed pH of 6.5. Atomic adsorption spectroscopy was utilized to detect the proportion of metals removed from water. Additionally, the pseudo-first-order, pseudo-second-order, Freundlich, and Langmuir models were employed to compute the kinetic and isothermic data from metal ion adsorption onto the adsorbents. The amino-functionalized adsorbent showed adsorption capacities of 277.008, 254.453, and 258.398 mg/g for Cu(II), Pb(II), and Zn(II) ions, respectively. According to the adsorption results, the Langmuir isotherm and the pseudo-second-order model best suit the data. The best fitting of the pseudo-second-order model with the data indicates that coordinative interactions between amino groups and metal ions are responsible for chemisorption. The metal ions bind with -NH2 groups on the adsorbent surface through chelate bonds. Chelate bonds are extremely strong and stable, indicating the effectiveness of the CoFe2O4@SiO2-NH2 adsorbent in adsorbing heavy-metal ions. The tested adsorbent exhibited good performance, batter stability, and good reusable values around 77, 81, and 76% for Cu(II), Pb(II), and Zn(II) ions, respectively, after five adsorption cycles.

Development and optimization of metoclopramide containing polymeric patches: impact of permeation enhancers

Abstract The study is aimed to develop a monolithic controlled matrix transdermal patches containing Metoclopramide as a model drug by solvent casting method. Eudragit L100, Polyvinylpyrrolidone K-30, and Methylcellulose were used in different ratios and Polyethylene glycol 400 added as a plasticizer. Resulting patches were evaluated for their physicochemical characters like organoleptic characters, weight variation, folding endurance, thickness, swelling index, flatness, drug content, swelling index, percentage erosion, moisture content, water vapor transmission rate and moisture uptake. Formed patches were also evaluated through Fourier transform spectroscopy (FT-IR), X-ray diffraction (XRD), Differential Scanning calorimetry (DSC) and Scanning Electron Microscopy (SEM). Results of SEM unveiled smooth surface of drug-loaded patches. In-vitro dissolution studies were conducted by using dissolution medium phosphate buffer saline pH 7.4. Effect of natural permeation enhancers was elucidated on two optimized formulations (Z4 and Z9). Different concentrations (5%-10 %) of permeation enhancers i.e. Olive oil, Castor oil and Eucalyptus oil were evaluated on Franz diffusion cell using excised abdominal rat skin. Z4-O2 (Olive oil 10%) had enhanced sustain effect and flux value (310.72) close to the desired flux value. Z4-O2 followed Higuchi release model (R2= 0.9833) with non-fickian diffusion release mechanism (n=0.612)