This study introduces a fractional order model to investigate the dynamics of polio disease spread, focusing on its significance, unique results, and conclusions. We emphasize the importance of understanding polio transmission dynamics and propose a novel approach using a fractional order model with an exponential decay kernel. Through rigorous analysis, including existence and stability assessment applying the Caputo Fabrizio fractional operator, we derive key insights into the disease dynamics. Our findings reveal distinct disease-free equilibrium (DFE) and endemic equilibrium (EE) points, shedding light on the disease\'s stability. Furthermore, graphical representations and numerical simulations demonstrate the behavior of the disease under various parameter values, enhancing our understanding of polio transmission dynamics. In conclusion, this study offers valuable insights into the spread of polio and contributes to the broader understanding of infectious disease dynamics.

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.
METHODS: 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.
CONCLUSIONS: 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.

The fundamental goal of this research is to suggest a novel mathematical operator for modeling visceral leishmaniasis, specifically the Caputo fractional-order derivative. By utilizing the Fractional Euler Method, we were able to simulate the dynamics of the fractional visceral leishmaniasis model, evaluate the stability of the equilibrium point, and devise a treatment strategy for the disease. The endemic and disease-free equilibrium points are studied as symmetrical components of the proposed dynamical model, together with their stabilities. It was shown that the fractional calculus model was more accurate in representing the situation under investigation than the classical framework at α = 0.99 and α = 0.98. We provide justification for the usage of fractional models in mathematical modeling by comparing results to real-world data and finding that the new fractional formalism more accurately mimics reality than did the classical framework. Additional research in the future into the fractional model and the impact of vaccinations and medications is necessary to discover the most effective methods of disease control.

UNASSIGNED: This study explores the dynamics of a mathematical model, utilizing ordinary differential equations (ODE), to depict the interplay between cancer cells and effector cells under chemotherapy. The stability of the equilibrium points in the model is analysed using the Jacobian matrix and eigenvalues. Additionally, bifurcation analysis is conducted to determine the optimal values for the control parameters.
UNASSIGNED: To evaluate the performance of the model and control strategies, benchmarking simulations are performed using the PlatEMO platform.
UNASSIGNED: The Pure Multi-objective Optimal Control Problem (PMOCP) and the Hybrid Multi-objective Optimal Control Problem (HMOCP) are two different forms of optimal control problems that are solved using revolutionary metaheuristic optimisation algorithms. The utilization of the Hypervolume (HV) performance indicator allows for the comparison of various metaheuristic optimization algorithms in their efficacy for solving the PMOCP and HMOCP.
UNASSIGNED: Results indicate that the MOPSO algorithm excels in solving the HMOCP, with M-MOPSO outperforming for PMOCP in HV analysis.
UNASSIGNED: Despite not directly addressing immediate clinical concerns, these findings indicates that the stability shifts at critical thresholds may impact treatment efficacy.

BACKGROUND: Hepatitis B is a potentially life-threatening infectious disease caused by the hepatitis B virus (HBV). Approximately 390,000 people in China die from HBV-related diseases each year. Around 86 million individuals suffer from infections of the hepatitis B virus, accounting for about 6% of the total population in the region. There are approximately 30 million chronic infections. From 2002 to 2007, China\'s government took part in \"The Global Alliance for Vaccines and Immunization (GAVI)\" initiative, which helped reduce cases of chronic HBV infections among children. However, incidences of hepatitis B remain persistently high in China. Accurately estimating the number of potential HBV infections is crucial for preventing and controlling the transmission of the hepatitis B virus. Up until now, there were no studies of potentially infectious hepatitis B virus infections.
METHODS: this study was based on data from the National Bureau of Statistics of China from 2003 to 2021; a dynamic model was built, which included a compartment for potentially infectious hepatitis B virus infections. The parameters in the model were fitted using a combination of nonlinear least-squares and genetic algorithm methods.
RESULTS: the calculated reproduction number for hepatitis B virus transmission within the population is Rc = 1.741. Considering the existing vaccine inefficiency rate of 0.1, the model estimates there are 449,535 (95%CI [415,651, 483,420]) potentially infectious hepatitis B virus infections, constituting 30.49% of total hepatitis B cases. Date fitting using MATLAB reveals that increasing the rate of hepatitis B vaccinations can effectively reduce the number of infections.
CONCLUSIONS: the results reveal that the number of potential infectious hepatitis B virus infections is so high that the number of hepatitis B patients persistently rises in China. To better control the transmission of the hepatitis B virus, an optional prevention and control strategy is needed to increase the vaccination of different age groups, and it is necessary to help the public correctly understand the transmission of hepatitis B and ensure adequate protection.

BACKGROUND: Topic models are a class of unsupervised machine learning models, which facilitate summarization, browsing and retrieval from large unstructured document collections. This study reviews several methods for assessing the quality of unsupervised topic models estimated using non-negative matrix factorization. Techniques for topic model validation have been developed across disparate fields. We synthesize this literature, discuss the advantages and disadvantages of different techniques for topic model validation, and illustrate their usefulness for guiding model selection on a large clinical text corpus.
UNASSIGNED: Using a retrospective cohort design, we curated a text corpus containing 382,666 clinical notes collected between 01/01/2017 through 12/31/2020 from primary care electronic medical records in Toronto Canada.
METHODS: Several topic model quality metrics have been proposed to assess different aspects of model fit. We explored the following metrics: reconstruction error, topic coherence, rank biased overlap, Kendall\'s weighted tau, partition coefficient, partition entropy and the Xie-Beni statistic. Depending on context, cross-validation and/or bootstrap stability analysis were used to estimate these metrics on our corpus.
RESULTS: Cross-validated reconstruction error favored large topic models (K ≥ 100 topics) on our corpus. Stability analysis using topic coherence and the Xie-Beni statistic also favored large models (K = 100 topics). Rank biased overlap and Kendall\'s weighted tau favored small models (K = 5 topics). Few model evaluation metrics suggested mid-sized topic models (25 ≤ K ≤ 75) as being optimal. However, human judgement suggested that mid-sized topic models produced expressive low-dimensional summarizations of the corpus.
CONCLUSIONS: Topic model quality indices are transparent quantitative tools for guiding model selection and evaluation. Our empirical illustration demonstrated that different topic model quality indices favor models of different complexity; and may not select models aligning with human judgment. This suggests that different metrics capture different aspects of model goodness of fit. A combination of topic model quality indices, coupled with human validation, may be useful in appraising unsupervised topic models.

BACKGROUND: The structures of Ag2n-1Sn- (n = 2-11) clusters are obtained by the combination of genetic algorithm (GA) and density functional theory (DFT). All the global minimum structures prefer hollow polyhedral structures, in which S-Ag-S element, triangular Ag3S3 and tetragonal Ag4S4 units present to stabilize the structures. The S atoms in the structures appear in μ3-S or μ4-S form. Adiabatic and vertical electron affinities of the clusters have been obtained, which reveals that they increases as cluster size. Stability analysis shows that Ag9S5- and Ag19S10- have special stability. The HOMO, LUMO orbitals of the clusters are obtained and the orbital components of them are calculated. The HOMO orbitals are mainly from the p orbitals of S atoms, whereas the s, p and d orbitals of Ag atoms contribute much bigger than the p orbitals of S atoms for LUMO orbitals. The orbital delocalization indexes (ODI) of the HOMOs and LUMOs are calculated, and the small ODIs of the HOMOs and LUMOs for n = 4-10 reveal that these orbitals are highly delocalized. By studying the projected density of states and molecular orbitals of Ag9S5- and Ag19S10- clusters, it is found that their molecular orbitals have superatomic properties. Superatomic properties play an important role in stabilizing clusters.
METHODS: This work used combined genetic algorithm and density functional theory (GA-DFT), and PBE0/Lanl2tz(Ag)/6-311G(d,p)(S) method to optimize the structures. Gaussian 16 program, Gauss view 6.0.16 program and Multiwfn 3.8 code are the softwares used.

UNASSIGNED: Ebola Virus causes disease both in human and non-human primates especially in developing countries. In 2014 during its outbreak, it led to majority of deaths especially in some impoverished area of West Africa and its effect is still witnessed up till date.
UNASSIGNED: We studied the spread of Ebola virus and obtained a system of equations comprising of eighteen equations which completely described the transmission of Ebola Virus in a population where control measures were incorporated and a major source of contacting the disease which is the traditional washing of dead bodies was also incorporated. We investigated the local stability of the disease-free equilibrium using the Jacobian Matrix approach and the disease- endemic stability using the center manifold theorem. We also investigated the global stability of the equilibrium points using the LaSalle\'s Invariant principle.
UNASSIGNED: The result showed that the disease-free and endemic equilibrium where both local and globally stable and that the system exhibits a forward bifurcation.
UNASSIGNED: Numerical simulations were carried out and our graphs show that vaccine and condom use is best for susceptible population, quarantine is best for exposed population, isolation is best for infectious population and proper burial of the diseased dead is the best to avoid further disease spread in the population and have quicker and better recovery.

Diabetes is sweeping the world as a silent epidemic, posing a growing threat to public health. Modeling diabetes is an effective method to monitor the increasing prevalence of diabetes and develop cost-effective strategies that control the incidence of diabetes and its complications. This paper focuses on a mathematical model known as the diabetes complication (DC) model. The DC model is analyzed using different numerical methods to monitor the diabetic population over time. This is by analyzing the model using five different numerical methods. Furthermore, the effect of the time step size and the various parameters affecting the diabetic situation is examined. The DC model is dependent on some parameters whose values play a vital role in the convergence of the model. Thus, parametric analysis was implemented and later discussed in this paper. Essentially, the Runge-Kutta (RK) method provides the highest accuracy. Moreover, Adam-Moulton\'s method also provides good results. Ultimately, a comprehensive understanding of the development of diabetes complications after diagnosis is provided in this paper. The results can be used to understand how to improve the overall public health of a country, as governments ought to develop effective strategic initiatives for the screening and treatment of diabetes.

The current manuscript studies a discrete-time phytoplankton-zooplankton model with Holling type-II response. The original model is modified by considering the condition that the phytoplankton population is getting infected with an external toxic substance. To obtain the discrete counterpart from a continuous-time system, Euler\'s forward method is applied. Moreover, a consistent discrete-time phytoplankton-zooplankton model is obtained by using a nonstandard difference scheme. The boundedness character for every positive solution is discussed, and the local stability of obtained system about each of its fixed points is discussed. The existence of period-doubling bifurcation at a positive equilibrium point is discussed for the discrete system obtained by Euler\'s forward method. In addition, the comparison of the consistent discrete-time version with its inconsistent counterpart is provided. It is proved that the discrete-time system obtained by using a nonstandard scheme is dynamically consistent as there is no chance for the existence of period-doubling bifurcation in that system. In order to control the period-doubling bifurcation and Neimark-Sacker bifurcation, an improved hybrid control strategy is applied. Finally, we have provided some interesting numerical examples to explain our theoretical results.