Cervical cancer is one of the most common types of cancer and it is caused mostly by high-risk Human Papillomavirus (HPV) and continues to spread at an alarming rate. While HPV impacts have been investigated before, there are currently only a scanty number of mathematical models that account for HPV\'s dynamic role in cervical cancer. The objectives were to develop an in-host density-dependent deterministic model for the dynamics implications of basal cells, virions, and lymphocytes incorporating immunity and functional responses. Analyze the model using techniques of epidemiological models such as basic reproduction number and simulate the model using Matlab ODE solver. Six compartments are considered in the model that is; Susceptible cells (S), Infected cells (I), Precancerous cells (P), Cancerous cells (C), Virions (V), and Lymphocytes (L). Next generation matrix (NGM), survival function, and characteristic polynomial method were used to determine the basic reproduction number denoted as R 0 . R 0 was obtained using three methods because NGM has some weaknesses hence the need for the other two methods. The findings from this research indicated that Disease-Free Equilibrium point is locally asymptotically stable whenever R 0 * < 1 and globally asymptotically stable if R 0 * ≤ 1 and the Endemic Equilibrium is globally asymptotically stable if R 0 * > 1 . The results obtained shows that the progression rate of precancerous cells to cancerous cells ( θ ) has the most direct impact on the model. The model was able to estimate the longevity of a patient as 10 days when ( θ ) increases by 0.08 . The findings of this research will help healthcare providers, public health authorities, and non-governmental health groups in creating effective prevention strategies to slow the development of cervical cancer. More research should be done to determine the exact number of cancerous cells that can lead to the death of a cervical cancer patient since this paper estimated a proportion of 75 % .

In the current study, we employ the novel fractal-fractional operator in the Atangana-Baleanu sense to investigate the dynamics of an interacting phytoplankton species model. Initially, we utilize the Picard-Lindelöf theorem to validate the uniqueness and existence of solutions for the model. We then explore equilibrium points within the phytoplankton model and conduct Hyers-Ulam stability analysis. Additionally, we present a numerical scheme utilizing the Newton polynomial to validate our analytical findings. Numerical simulations illustrate the dynamical behavior of the model across various fractal and fractional parameter values, visualized through graphical representations. Our simulations reveal that the stability of equilibrium points is not significantly impacted with the long-term memory effect, which is characterized by fractal-fractional order values. However, an increase in fractal-fractional parameters accelerates the convergence of solutions to their intended equilibrium states.

The resurgence of monkeypox causes considerable healthcare risks needing efficient immunization programs. This work investigates the monkeypox disease dynamics in the UK, focusing on the impact of vaccination under real data. The key difficulty is to correctly predict the spread of the disease and evaluate the success of immunization efforts. We construct a mathematical model for monkeypox infection and extend it to the fractional case considering the Caputo derivative. The analysis ensures the positivity, boundedness, and uniqueness of the solution for the non-integer system. We conduct a local asymptotical stability analysis (LAS) at the disease-free equilibrium (DFE) D0, showing the result for R0<1. Additionally, we demonstrate the existence of multiple endemic equilibria and provide conditions for backward bifurcation, which are illustrated graphically. Using real case data from the UK, we estimate model parameters via the nonlinear least square method. Our results show that, without vaccination, R2≈0.8, whereas vaccination reduces it to R2v=0.48. We perform sensitivity analysis to identify key parameters influencing disease elimination, presenting the outcomes through graphs. To solve numerically the fractional model, we outline a numerical scheme and provide detailed results under various parameter assumptions. Our findings suggest that high vaccine efficacy, a low waning rate of the vaccines, and increased vaccination of the infected people can significantly reduce the future cases of monkeypox in the UK. The present study offers a comprehensive framework for monkeypox dynamics and informs public health strategies for effective disease control and prevention.

OBJECTIVE: The tumor microenvironment (TME) plays a crucial role in tumor progression and treatment response. Radiomics offers a non-invasive approach to studying the TME by extracting quantitative features from medical images. In this study, we present a novel approach to assess the stability and discriminative ability of radiomics features in the TME of vestibular schwannoma (VS).
METHODS: Magnetic Resonance Imaging (MRI) data from 242 VS patients were analyzed, including contrast-enhanced T1-weighted (ceT1) and high-resolution T2-weighted (hrT2) sequences. Radiomics features were extracted from concentric peri-tumoral regions of varying sizes. The intraclass correlation coefficient (ICC) was used to assess feature stability and discriminative ability, establishing quantile thresholds for ICCmin and ICCmax.
RESULTS: The identified thresholds for ICCmin and ICCmax were 0.45 and 0.72, respectively. Features were classified into four categories: stable and discriminative (S-D), stable and non-discriminative (S-ND), unstable and discriminative (US-D), and unstable and non-discriminative (US-ND). Different feature groups exhibited varying proportions of S-D features across ceT1 and hrT2 sequences. The similarity of S-D features between ceT1 and hrT2 sequences was evaluated using Jaccard\'s index, with a value of 0.78 for all feature groups which is ranging from 0.68 (intensity features) to 1.00 (Neighbouring Gray Tone Difference Matrix (NGTDM) features).
CONCLUSIONS: This study provides a framework for identifying stable and discriminative radiomics features in the TME, which could serve as potential biomarkers or predictors of patient outcomes, ultimately improving the management of VS patients.

BACKGROUND: PfK13 protein mutations are associated with the emergence of artemisinin resistance in Plasmodium falciparum. PfK13 protein is essential for mediating ubiquitination and controlling the PI3K/AKT pathway. Mutant PfK13 variations can interfere with substrate binding, especially with PfPI3K, which raises PfPI3K levels.
METHODS: DUET, DynaMut2, mCSM, iStable 2.0, I-Mutant 2.0, and MuPro were utilized to study the protein stability and protein-substrate binding was studied using HADDOCK 2.4 docking algorithm between Wild-type and mutant PfK13 with the helical and catalytic domain of PfPI3K.
RESULTS: i-Stable server analysis predicted that seven, out of the nine mutations associated with artemisinin resistance (F446I, Y493H, R539T, I543T, P553L, R561H, C580Y) reduced the protein stability. HADDOCK scores of the catalytic domain underscores the significant impact of the reported mutations on the binding affinity of the PfK13 protein. Further validation through the MM_GBSA technique, the binding free energy (DDG) between the wild-type and the mutant PfK13 protein analysis revealed a loss of interactions resulting from mutations in PfK13.
CONCLUSIONS: The study finding suggest that mutations in the PfK13 cause destabilization in the protein structure and affects the binding of PfPI3K. Although the findings remain preliminary and require further validation, it provides the basis for further research considering the importance of the interaction of PfK13 and PfPI3K to overcome the impact of artemisinin resistance.

The COVID-19 pandemic came with many setbacks, be it to a country\'s economy or the global missions of organizations like WHO, UNICEF or GTFCC. One of the setbacks is the rise in cholera cases in developing countries due to the lack of cholera vaccination. This model suggested a solution by introducing another public intervention, such as adding Chlorine to water bodies and vaccination. A novel delay differential model of fractional order was recommended, with two different delays, one representing the latent period of the disease and the other being the delay in adding a disinfectant to the aquatic environment. This model also takes into account the population that will receive a vaccination. This study utilized sensitivity analysis of reproduction number to analytically prove the effectiveness of control measures in preventing the spread of the disease. This analysis provided the mathematical evidence for adding disinfectants in water bodies and inoculating susceptible individuals. The stability of the equilibrium points has been discussed. The existence of stability switching curves is determined. Numerical simulation showed the effect of delay, resulting in fluctuations in some compartments. It also depicted the impact of the order of derivative on the oscillations.

In recent years, numerous attempts have been made to develop a low-cost adsorbent for selectively recovering industrially important products from fermentation broth or complex mixtures. The current study is a novel attempt to selectively adsorb esterase from Trichoderma harzianum using cheap adsorbents like bentonite (BT), activated charcoal (AC), silicon dioxide (SiO2), and titanium dioxide (TiO2). AC had the highest esterase adsorption of 97.58% due to its larger surface area of 594.45 m3/g. SiO2 was found to have the highest selectivity over esterase, with an estimated purification fold of 7.2. Interestingly, the purification fold of 5.5 was found in the BT-extracted fermentation broth. The functional (FT-IR) and morphological analysis (SEM-EDX) were used to characterize the adsorption of esterase. Esterase adsorption on AC, SiO2, and TiO2 was well fitted by Freundlich isotherm, demonstrating multilayer adsorption of esterase. A pseudo-second-order kinetic model was developed for esterase adsorption in various adsorbents. Thermodynamic analysis revealed that adsorption is an endothermic process. AC has the lowest Gibbs free energy of -10.96 kJ/mol, which supports the spontaneous maximum adsorption of both esterase and protein. In the desorption study, the maximum recovery of esterase from TiO2 using sodium chloride was 41.34 %. Unlike other adsorbents, the AC-adsorbed esterase maintained its catalytic activity and stability, implying that it could be used as an immobilization system for commercial applications. According to the kinetic analysis, the overall rate of the reaction was controlled by reaction kinetics rather than external mass transfer resistance, as indicated by the Damkohler number.

The motivation for constructing a thin-shell wormhole from a (2+1)-dimensional rotating black hole arises from the desire to study the effects of a nonminimally coupled scalar field in this particular spacetime. By investigating the behavior of such a field in the presence of rotation, we can gain insights into the interplay between gravity and scalar fields in lower-dimensional systems. Additionally, this construction allows us to explore potential connections between black hole physics and exotic phenomena like traversable wormholes. The radial perturbation around the equilibrium throat radius is considered to explore the stable configuration for specific values of physical parameters. Then, the equations of state, specifically the phantom-like and generalized Chaplygin gas model for exotic matter is used to conduct an extensive investigation into the stability of the counter-rotating thin-shell wormholes. Our results show that the presence of a scalar field enhances the stability of the counter-rotating thin-shell wormholes.

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.

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.