Modeling and analysis of a human papilloma virus transmission model with impact of media.

The human papillomavirus (HPV) is threatening human health as it spreads globally in varying degrees. On the other hand, the speed and scope of information transmission continues to increase, as well as the significant increase in the number of HPV-related news reports, it has never been more important to explore the role of media news coverage in the spread and control of the virus. Using a decreasing factor that captures the impact of media on the actions of people, this paper develops a model that characterizes the dynamics of HPV transmission with media impact, vaccination and recovery. We obtain global stability of equilibrium points employing geometric method, and further yield effective methods to contain the HPV pandemic by sensitivity analysis. With the center manifold theory, we show that there is a forward bifurcation when R0=1. Our study suggested that, besides controlling contact between infected and susceptible populations and improving effective vaccine coverage, a better intervention would be to strengthen media coverage. In addition, we demonstrated that contact rate and the effect of media coverage result in multiple epidemics of infection when certain conditions are met, implying that interventions need to be tailored to specific situations.

Evolutionary game analysis between regional governments and shipping companies: Considering the impact of government subsidy on shipping companies.

Maritime agencies are imposing stricter limits on fuel sulfur content, and regional governments are encouraging the reduction of various emissions through subsidies. In this study, an evolutionary game model is constructed to analyze the interaction between regional governments and shipping companies under the fixed and dynamic subsidies. The sensitivity analysis reveals the effect of parameters on stabilization strategies. The results show that the bilateral stakeholders can adopt stabilization strategies under dynamic subsidies. The fines, maximum subsidies and extra cost paid by regional governments have a significant impact on these strategies. To reduce the dependence of shipping companies on subsidy policies, it is recommended to improve the LSFO refining technology in the future. Expanding the implementation scope of LSFO subsidy policies will increase the utilization of LSFO by shipping companies. This study offers insights for governments to optimize the LSFO subsidy policy and shipping companies to choose sulfur oxides reduction approaches.

Machine learning prediction of methane, nitrogen, and natural gas mixture viscosities under normal and harsh conditions.

The accurate estimation of gas viscosity remains a pivotal concern for petroleum engineers, exerting substantial influence on the modeling efficacy of natural gas operations. Due to their time-consuming and costly nature, experimental measurements of gas viscosity are challenging. Data-based machine learning (ML) techniques afford a resourceful and less exhausting substitution, aiding research and industry at gas modeling that is incredible to reach in the laboratory. Statistical approaches were used to analyze the experimental data before applying machine learning. Seven machine learning techniques specifically Linear Regression, random forest (RF), decision trees, gradient boosting, K-nearest neighbors, Nu support vector regression (NuSVR), and artificial neural network (ANN) were applied for the prediction of methane (CH4), nitrogen (N2), and natural gas mixture viscosities. More than 4304 datasets from real experimental data utilizing pressure, temperature, and gas density were employed for developing ML models. Furthermore, three novel correlations have developed for the viscosity of CH4, N2, and composite gas using ANN. Results revealed that models and anticipated correlations predicted methane, nitrogen, and natural gas mixture viscosities with high precision. Results designated that the ANN, RF, and gradient Boosting models have performed better with a coefficient of determination (R2) of 0.99 for testing data sets of methane, nitrogen, and natural gas mixture viscosities. However, linear regression and NuSVR have performed poorly with a coefficient of determination (R2) of 0.07 and - 0.01 respectively for testing data sets of nitrogen viscosity. Such machine learning models offer the industry and research a cost-effective and fast tool for accurately approximating the viscosities of methane, nitrogen, and gas mixture under normal and harsh conditions.

How many Monte Carlo samples are needed for probabilistic cost-effectiveness analyses?

OBJECTIVE: Probabilistic sensitivity analysis (PSA) is conducted to account for the uncertainty in cost and effect of decision options under consideration. PSA involves obtaining a large sample of input parameter values (N) to estimate the expected cost and effect of each alternative in the presence of parameter uncertainty. When the analysis involves using stochastic models (e.g., individual-level models), the model is further replicated P times for each sampled parameter set. We study how N and P should be determined. METHODS: We show that PSA could be structured such that P can be an arbitrary number (say, P=1). To determine N, we derive a formula based on Chebyshev's inequality such that the error in estimating the incremental cost-effectiveness ratio (ICER) of alternatives (or equivalently, the willingness-to-pay value at which the optimal decision option changes) is within a desired level of accuracy. We described two methods to confirmed, visually and quantitatively, that the N informed by this method results in ICER estimates within the specified level of accuracy. RESULTS: When N is arbitrarily selected, the estimated ICERs could be substantially different from the true ICER (even as P increases), which could lead misleading conclusions. Using a simple resource allocation model, we demonstrate that the proposed approach can minimize the potential for this error. CONCLUSIONS: The number of parameter samples in probabilistic CEAs should not be arbitrarily selected. We describe three methods to ensure that enough parameter samples are used in probabilistic CEAs.

A mathematical model for wound healing in the reef-building coral Pocillopora damicornis.

Coral reefs, among the most diverse ecosystems on Earth, currently face major threats from pollution, unsustainable fishing practices , and perturbations in environmental parameters brought on by climate change. Corals also sustain regular wounding from other sea life and human activity. Recent reef restoration practices have even involved intentional wounding by systematically breaking coral fragments and relocating them to revitalize damaged reefs, a practice known as microfragmentation. Despite its importance, very little research has explored the inner mechanisms of wound healing in corals. Some reef-building corals have been observed to initiate an immunological response to wounding similar to that observed in mammalian species. Utilizing prior models of wound healing in mammalian species as the mathematical basis, we formulated a mechanistic model of wound healing, including observations of the immune response and tissue repair in scleractinian corals for the species Pocillopora damicornis. The model consists of four differential equations which track changes in remaining wound debris, number of cells involved in inflammation, number of cells involved in proliferation, and amount of wound closure through re-epithelialization. The model is fit to experimental wound size data from linear and circular shaped wounds on a live coral fragment. Mathematical methods, including numerical simulations and local sensitivity analysis, were used to analyze the resulting model. The parameter space was also explored to investigate drivers of other possible wound outcomes. This model serves as a first step in generating mathematical models for wound healing in corals that will not only aid in the understanding of wound healing as a whole, but also help optimize reef restoration practices and predict recovery behavior after major wounding events.

Fuzzy random sensitivity analysis for the overall structure reliability of reinforced concrete freezing wellbores in deep alluvium based on hidden Markov model.

To address the shortcomings of traditional reliability theory in characterizing the stability of deep underground structures, the advanced first order second moment of reliability was improved to obtain fuzzy random reliability, which is more consistent with the working conditions. The traditional sensitivity analysis model was optimized using fuzzy random optimization, and an analytical calculation model of the mean and standard deviation of the fuzzy random reliability sensitivity was established. A big data hidden Markov model and expectation-maximization algorithm were used to improve the digital characteristics of fuzzy random variables. The fuzzy random sensitivity optimization model was used to confirm the effect of concrete compressive strength, thick-diameter ratio, reinforcement ratio, uncertainty coefficient of calculation model, and soil depth on the overall structural reliability of a reinforced concrete double-layer wellbore in deep alluvial soil. Through numerical calculations, these characteristics were observed to be the main influencing factors. Furthermore, while the soil depth was negatively correlated, the other influencing factors were all positively correlated with the overall reliability. This study provides an effective reference for the safe construction of deep underground structures in the future.

Economic evaluation of submerged anaerobic hybrid membrane bioreactor operating at mesophilic temperature.

A laboratory-scale mesophilic submerged anaerobic hybrid membrane bioreactor (An-HMBR) was operated for 270 days for the treatment of high-strength synthetic wastewater at different hydraulic retention times (HRTs) (3 days, 2 days, 1 day, and 0.5 days). Chemical oxygen demand (COD) removal efficiency of 92% was obtained with methane yield rate of 0.18 LCH4/g CODremoval at 1-day HRT. The results of lab scale reactor at 1-day HRT were utilized for upscaling and cost analysis. Cost analysis revealed that the total capital cost comprised tank system (48%), membrane cost (32%), screen and PUF sponge (5% each), PLCs (4%), liquid pumps (3%), and others (2%). The operational cost comprised chemical cost (46%), pumping energy (42%), and sludge disposal (12%). The results revealed that the tank and heating costs accounted for the largest fraction of the total life cycle cost for full-scale An-HMBR. The heating cost can be compensated by gas recovery. Sensitivity analysis revealed that the interest rates, influent flow, and membrane flux were the most crucial parameters which affected the total cost of An-HMBR.

NITIRSOIL: A model that balances complexity with prediction uncertainty for improving nitrogen fertilization in agriculture.

Mismanagement of the nitrogen (N) fertilization in agriculture leads to low N use efficiency (NUE) and therefore pollution of waters and atmosphere due to NO3- leaching, and N2O and NH3 emissions. The use of N simulation models of the soil-plant system can help improve the N fertilizer management increasing NUE and decreasing N pollution issues. However, many N simulation models lack balance between complexity and uncertainty with the result that they are not applied in actual practice. The NITIRSOIL is a one-dimensional transient-state model with a monthly time step that aims at addressing this lack in the estimation of, mainly, dry matter yield (DMY), crop N uptake (Nupt), soil mineral N (Nmin), and NO3- leaching in agricultural fields. According to its global sensitivity analysis for horticulture, the NITIRSOIL simulations of the aforementioned outputs mostly depend on the critical N dilution curve, harvest index, dry matter fraction, potential fresh yield and nitrification coefficients. According to its validation for 35 nitrogen fertilization trials with 11 vegetables under semi-arid Mediterranean climate in Eastern Spain, the NITIRSOIL presents indices of agreement between 0.87 and 0.97 for the prediction of total dry matter, DMY, Nupt, NO3- leaching and soil Nmin at crop season end. Therefore, the NITIRSOIL model can be used in actual practice to improve the sustainability of the N management in, particularly horticulture, due to the balance it features between complexity and prediction uncertainty. For this aim, the NITRISOIL can be used either on its own, or in combination with "Nmin" on-site N fertilization recommendation methods, or even could be implemented as the calculation core of decision support systems.

Improving groundwater vulnerability assessment in structurally controlled hard rock aquifer: insight from lineament density and land use/land cover pattern.

A comprehensive seasonal assessment of groundwater vulnerability was conducted in the weathered hard rock aquifer of the upper Swarnrekha watershed in Ranchi district, India. Lineament density (Ld) and land use/land cover (LULC) were integrated into the conventional DRASTIC and Pesticide DRASTIC (P-DRASTIC) models and were extensively compared with six modified models, viz. DRASTIC-Ld, DRASTIC-Lu, DRASTIC-LdLu, P-DRASTIC-Ld, P-DRASTIC-Lu, and P-DRASTIC-LdLu, to identify the most optimal model for vulnerability mapping in hard rock terrain of the region. Findings were geochemically validated using NO3- concentrations of 68 wells during pre-monsoon (Pre-M) and post-monsoon (Post-M) 2022. Irrespective of the applied model, groundwater vulnerability shows significant seasonal variation, with > 45% of the region classified as high to very high vulnerability in the pre-M, increasing to Ì´67% in post-M season, highlighting the importance of seasonal vulnerability assessments. Agriculture and industries' dominant southern region showed higher vulnerability, followed by regions with high Ld and thin weathered zone. Incorporating Ld and LULC parameters into DRASTIC-LdLu and P-DRASTIC-LdLu models increases the 'Very High' vulnerability zones to 17.4% and 17.6% for pre-M and 29.4% and 27.9% for post-M, respectively. Similarly, 'High' vulnerable zones increase from 32.5% and 25% in pre-M to 33.8% and 35.3% in post-M for respective models. Model output comparisons suggest that modified DRASTIC-LdLu and P-DRASTIC-LdLu perform better, with accurate estimations of 83.8% and 89.7% for pre-M and post-M, respectively. However, results of geochemical validation suggest that among all the applied modified models, DRASTIC-LdLu performs best, with accurate estimations of 34.4% and 20.6% for pre-M and post-M, respectively.

Physics-informed machine learning algorithms for forecasting sediment yield: an analysis of physical consistency, sensitivity, and interpretability.

The sediment transport, involving the movement of the bedload and suspended sediment in the basins, is a critical environmental concern that worsens water scarcity and leads to degradation of land and its ecosystems. Machine learning (ML) algorithms have emerged as powerful tools for predicting sediment yield. However, their use by decision-makers can be attributed to concerns regarding their consistency with the involved physical processes. In light of this issue, this study aims to develop a physics-informed ML approach for predicting sediment yield. To achieve this objective, Gaussian, Center, Regular, and Direct Copulas were employed to generate virtual combinations of physical of the sub-basins and hydrological datasets. These datasets were then utilized to train deep neural network (DNN), conventional neural network (CNN), Extra Tree, and XGBoost (XGB) models. The performance of these models was compared with the modified universal soil loss equation (MUSLE), which serves as a process-based model. The results demonstrated that the ML models outperformed the MUSLE model, exhibiting improvements in Nash-Sutcliffe efficiency (NSE) of approximately 10%, 18%, 32%, and 41% for the DNN, CNN, Extra Tree, and XGB models, respectively. Furthermore, through Sobol sensitivity and Shapley additive explanation-based interpretability analyses, it was revealed that the Extra Tree model displayed greater consistency with the physical processes underlying sediment transport as modeled by MUSLE. The proposed framework provides new insights into enhancing the accuracy and applicability of ML models in forecasting sediment yield while maintaining consistency with natural processes. Consequently, it can prove valuable in simulating process-related strategies aimed at mitigating sediment transport at watershed scales, such as the implementation of best management practices.

Suicide Death Prediction Using the Maryland Suicide Data Warehouse: A Sensitivity Analysis.

OBJECTIVE: Nearly 50,000 Americans die each year from suicide, despite suicide death being a rare event in the context of health risk assessment and modeling. Prior research has underscored the need for contextualizing suicide risk models in terms of their potential uses and generalizability. This sensitivity analysis makes use of the Maryland Suicide Data Warehouse (MSDW) and illustrates how results inform clinical decision support. METHOD: A cohort of 1 million living control patients were extracted from the MSDW in addition to 1,667 patients who had died by suicide between the years 2016 and 2019 according to the Maryland Office of the Medical Examiner (OCME). Data were extracted and aggregated as part of a 4-year retrospective design. Binary logistic and two penalized regression models were deployed in a repeated fivefold cross-validation. Model performances were evaluated using sensitivity, positive predictive value (PPV), and F1, and model coefficients were ranked according to coefficient size. RESULTS: Several features were significantly associated with patients having died by suicide, including male sex, depressive and anxiety disorder diagnoses, social needs, and prior suicidal ideation and suicide attempt. Cross-validated binary logistic regression outperformed either ridge or LASSO (least absolute shrinkage and selection operator) models but generally achieved low-to-moderate PPV and sensitivity across most thresholds and a peak F1 of 0.323. CONCLUSIONS: Suicide death prediction is constrained by the context of use, which determines the best balance of precision and recall. Predictive models must be evaluated close to the level of intervention. They may not hold up to different needs at different levels of care.

Screening rate constants in the simulation of rapid kinetics of chlorophyll a fluorescence using the Morris method.

Chlorophyll a fluorescence, a sensitive and cost-effective probe, is widely used in photosynthetic research. Its rapid phase, occurring within 1 second under intense illumination, displays complex O-J-I-P transients, providing valuable insights into various aspects of photosynthesis. In addition to employing experimental approaches to measure the rapid Fluorescence Induction (FI) kinetics, mathematical modeling serves as a crucial tool for understanding the underlying mechanisms that drive FI dynamics. However, the significant uncertainty and arbitrary nature of selecting model parameters amplify concerns about the effectiveness of modeling tools in aiding photosynthesis research. Therefore, there is a need to gain a deeper understanding of how these models operate and how arbitrary parameter choices may influence their outcomes. In this study, we employed the Morris method, a global Sensitivity Analysis (SA) tool, to assess the significance of rate constants employed in an existing fluorescence model, particularly those linked to the entire electron transport chain, in shaping the rapid FI dynamics. In summary, utilizing the insights gained from the Morris SA allows for targeted refinement of the photosynthesis model, thereby improving our understanding of the complex processes inherent in photosynthetic systems.

Mathematical Assessment of the Role of Intervention Programs for Malaria Control.

Malaria remains a global health problem despite the many attempts to control and eradicate it. There is an urgent need to understand the current transmission dynamics of malaria and to determine the interventions necessary to control malaria. In this paper, we seek to develop a fit-for-purpose mathematical model to assess the interventions needed to control malaria in an endemic setting. To achieve this, we formulate a malaria transmission model to analyse the spread of malaria in the presence of interventions. A sensitivity analysis of the model is performed to determine the relative impact of the model parameters on disease transmission. We explore how existing variations in the recruitment and management of intervention strategies affect malaria transmission. Results obtained from the study imply that the discontinuation of existing interventions has a significant effect on malaria prevalence. Thus, the maintenance of interventions is imperative for malaria elimination and eradication. In a scenario study aimed at assessing the impact of long-lasting insecticidal nets (LLINs), indoor residual spraying (IRS), and localized individual measures, our findings indicate that increased LLINs utilization and extended IRS coverage (with longer-lasting insecticides) cause a more pronounced reduction in symptomatic malaria prevalence compared to a reduced LLINs utilization and shorter IRS coverage. Additionally, our study demonstrates the impact of localized preventive measures in mitigating the spread of malaria when compared to the absence of interventions.

Prevalence of male DNA on female worn undergarments. How small datasets may support robust opinions in activity level evaluative reporting.

In cases of sexual assault, the interpretation of biological traces on clothing, and particularly undergarments, may be complex. This is especially so when the complainant and defendant interact socially, for instance as (ex-)partners or by co-habitation. Here we present the results from a study where latent male DNA on female worn undergarments is recovered in four groups with different levels of male-female social interaction. The results conform to prior expectation, in that less interaction tend to result in less male DNA on undergarments. We explore the use of these experimental data for evaluative reporting given activity level propositions in a mock case scenario. We show how the selection of different populations to represent the social interaction between complainant and defendant may affect the strength of the evidence. We further show how datasets of limited size can be used for robust activity level evaluative reporting.

Development of similar materials for fluid-solid coupling model testing and application in damage constitutive models.

In order to provide suitable material selection for such fluid-solid coupling model tests, orthogonal experimental studies were conducted using iron concentrate powder and barite powder as aggregates, cement as cementitious materials, and gypsum and clay as modifiers. This research showed: (1) The ATC plays a dominant role in controlling the strength indexes and water absorption of the material, and these indexes show a significant decrease with the increase of the bone adhesive ratio. For each level of ATC increase, the compressive strength decreases by 0.2 MPa, the elastic modulus decreases by 10-20 MPa, and the cohesion decreases by 25-45 kPa. (2) Mixing gypsum and cement cannot jointly promote strength growth. (3) With the increase of GTC, the water absorption rate of the material increases, while the softening coefficient and permeability coefficient decrease obviously. Gypsum, which accounts for 4-16% of cement content, can be suitable for studying the hydraulic properties of similar materials for most sedimentary rock. Based on Weibull statistical damage theory, a damage constitutive model for the entire process of rock triaxial compression under the combined action of rainwater infiltration and load was established. Due to the influence of internal pores, the experimental and theoretical results have a certain deviation, the higher the confining pressure, the more obvious the deviation. In addition, the higher the rock strength, the less obvious the deviation caused by pores. This damage model can better describe the progressive failure process of rocks after rainwater infiltration, and can provide theoretical reference for the study of slope stability caused by rainwater infiltration.

Prediction of CO2 solubility in Ionic liquids for CO2 capture using deep learning models.

Ionic liquids (ILs) are highly effective for capturing carbon dioxide (CO2). The prediction of CO2 solubility in ILs is crucial for optimizing CO2 capture processes. This study investigates the use of deep learning models for CO2 solubility prediction in ILs with a comprehensive dataset of 10,116 CO2 solubility data in 164 kinds of ILs under different temperature and pressure conditions. Deep neural network models, including Artificial Neural Network (ANN) and Long Short-Term Memory (LSTM), were developed to predict CO2 solubility in ILs. The ANN and LSTM models demonstrated robust test accuracy in predicting CO2 solubility, with coefficient of determination (R2) values of 0.986 and 0.985, respectively. Both model's computational efficiency and cost were investigated, and the ANN model achieved reliable accuracy with a significantly lower computational time (approximately 30 times faster) than the LSTM model. A global sensitivity analysis (GSA) was performed to assess the influence of process parameters and associated functional groups on CO2 solubility. The sensitivity analysis results provided insights into the relative importance of input attributes on output variables (CO2 solubility) in ILs. The findings highlight the significant potential of deep learning models for streamlining the screening process of ILs for CO2 capture applications.

Sensitivity analysis for principal ignorability violation in estimating complier and noncomplier average causal effects.

An important strategy for identifying principal causal effects (popular estimands in settings with noncompliance) is to invoke the principal ignorability (PI) assumption. As PI is untestable, it is important to gauge how sensitive effect estimates are to its violation. We focus on this task for the common one-sided noncompliance setting where there are two principal strata, compliers and noncompliers. Under PI, compliers and noncompliers share the same outcome-mean-given-covariates function under the control condition. For sensitivity analysis, we allow this function to differ between compliers and noncompliers in several ways, indexed by an odds ratio, a generalized odds ratio, a mean ratio, or a standardized mean difference sensitivity parameter. We tailor sensitivity analysis techniques (with any sensitivity parameter choice) to several types of PI-based main analysis methods, including outcome regression, influence function (IF) based and weighting methods. We discuss range selection for the sensitivity parameter. We illustrate the sensitivity analyses with several outcome types from the JOBS II study. This application estimates nuisance functions parametrically - for simplicity and accessibility. In addition, we establish rate conditions on nonparametric nuisance estimation for IF-based estimators to be asymptotically normal - with a view to inform nonparametric inference.

Evaluating the impact of double dose vaccination on SARS-CoV-2 spread through optimal control analysis.

This paper presents a new nonlinear epidemic model for the spread of SARS-CoV-2 that incorporates the effect of double dose vaccination. The model is analyzed using qualitative, stability, and sensitivity analysis techniques to investigate the impact of vaccination on the spread of the virus. We derive the basic reproduction number and perform stability analysis of the disease-free and endemic equilibrium points. The model is also subjected to sensitivity analysis to identify the most influential model parameters affecting the disease dynamics. The values of the parameters are estimated with the help of the least square curve fitting tools. Finally, the model is simulated numerically to assess the effectiveness of various control strategies, including vaccination and quarantine, in reducing the spread of the virus. Optimal control techniques are employed to determine the optimal allocation of resources for implementing control measures. Our results suggest that increasing the vaccination coverage, adherence to quarantine measures, and resource allocation are effective strategies for controlling the epidemic. The study provides valuable insights into the dynamics of the pandemic and offers guidance for policymakers in formulating effective control measures.

Immune cell signatures and causal association with irritable bowel syndrome: A mendelian randomization study.

BACKGROUND: The mucosal barrier's immune-brain interactions, pivotal for neural development and function, are increasingly recognized for their potential causal and therapeutic relevance to irritable bowel syndrome (IBS). Prior studies linking immune inflammation with IBS have been inconsistent. To further elucidate this relationship, we conducted a Mendelian randomization (MR) analysis of 731 immune cell markers to dissect the influence of various immune phenotypes on IBS. Our goal was to deepen our understanding of the disrupted brain-gut axis in IBS and to identify novel therapeutic targets. AIM: To leverage publicly available data to perform MR analysis on 731 immune cell markers and explore their impact on IBS. We aimed to uncover immunophenotypic associations with IBS that could inform future drug development and therapeutic strategies. METHODS: We performed a comprehensive two-sample MR analysis to evaluate the causal relationship between immune cell markers and IBS. By utilizing genetic data from public databases, we examined the causal associations between 731 immune cell markers, encompassing median fluorescence intensity, relative cell abundance, absolute cell count, and morphological parameters, with IBS susceptibility. Sensitivity analyses were conducted to validate our findings and address potential heterogeneity and pleiotropy. RESULTS: Bidirectional false discovery rate correction indicated no significant influence of IBS on immunophenotypes. However, our analysis revealed a causal impact of IBS on 30 out of 731 immune phenotypes (P < 0.05). Nine immune phenotypes demonstrated a protective effect against IBS [inverse variance weighting (IVW) < 0.05, odd ratio (OR) < 1], while 21 others were associated with an increased risk of IBS onset (IVW ≥ 0.05, OR ≥ 1). CONCLUSION: Our findings underscore a substantial genetic correlation between immune cell phenotypes and IBS, providing valuable insights into the pathophysiology of the condition. These results pave the way for the development of more precise biomarkers and targeted therapies for IBS. Furthermore, this research enriches our comprehension of immune cell roles in IBS pathogenesis, offering a foundation for more effective, personalized treatment approaches. These advancements hold promise for improving IBS patient quality of life and reducing the disease burden on individuals and their families.

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.