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In this article, a modular model is proposed for the reliability modeling of phased mission systems (PMSs) with complicated system behaviors. By the modular method, the system is divided into several levels: system, subsystem, and components. At the component level, the shock effect, including self‐degradation, additional wear and damage caused by shocks, is considered and the component reliability is evaluated. Then, the reliability modeling method of the K/N system consisting of multiple K/N subsystems is proposed, by a mathematics reasoning method. The correctness of the proposed method is also verified by a Monte Carlo (MC) simulation procedure. At last, the modular method is applied at the system level, and the reliability of a practical engineering case, the attitude and orbit control system (AOCS), is evaluated for illustration. Meanwhile, the parameter sensitivity analysis is also carried out for implementation. [ABSTRACT FROM AUTHOR]

Turntable ladders are flexible large-scale manipulators, so an active oscillation damping is highly valuable. Aiming to support the development and parametrization of the controller, a precise dynamic model of the vehicle is desired. Previous work considering solely the dynamic oscillations of the ladder parts is extended by a dynamic model of the chassis and support structure that includes flexible deformation of the chassis. All contact forces to the ground are calculated because they provide potential for determining dynamic outreach limits in future. As it can happen in practice, the outriggers are able to become fully unloaded in the simulation model. This behaviour is validated by measurements. A sensitivity analysis is used to establish a suitable approach for identification of model parameters. Dynamical measurements illustrate that the combination of two dynamic models of ladder and chassis improves representation of the dynamic oscillations that are crucial for the active oscillation damping control.

In this study, a fractional-order mathematical model of the transmission dynamics of drug-resistant tuberculosis within a two-patch system incorporating population migration was proposed and analyzed using the Caputo operator. The positivity, boundedness, existence, and uniqueness of the solutions as well as the Ulam-Hyers stability of the model were guaranteed. Additionally, the basic reproduction numbers were derived and analyzed for sensitivity to identify the key parameters that affected the spread of drug-resistant tuberculosis. Moreover, the cure rates were used as control variables to formulate an optimal control problem, which examined the efficacy of the control measures and the influence of fractional order on the control values. The numerical results showed that controlling the cure rate can significantly reduce the number of drug-resistant tuberculosis infections, thus verifying the effectiveness of the proposed control strategy. As the fractional order decreased, the duration during which the maximum control intensity was applied in both patches increased.

In this article, we presented two novel approaches for group decision-making (GDM) that were derived from the initiated linguistic $ q $-rung orthopair fuzzy Aczel-Alsina weighted arithmetic (L$ q $-ROFAAWA) aggregation operator (AgOp) using linguistic $ q $-rung orthopair fuzzy numbers (L$ q $-ROFNs). To introduce these GDM techniques, we first defined new operational laws for L$ q $-ROFNs based on Aczel-Alsina $ t $-norm and $ t $-conorm. The developed scalar multiplication and addition operations of L$ q $-ROFNs addressed the limitations of operations when $ q = 1 $. The first proposed GDM methodology assumed that both experts' weights and attribute weights were fully known, while the second technique assumed that both sets of weights were entirely unknown. We also discussed properties of L$ q $-ROFNs under the L$ q $-ROFAAWA operators, such as idempotency, boundedness, and monotonicity. Furthermore, we solved problems related to environmental and economic issues, such as ranking countries by air pollution, selecting the best company for bank investments, and choosing the best electric vehicle design. Finally, we validated the proposed GDM approaches using three validity tests and performed a sensitivity analysis to compare them with preexisting models.

Tuberculosis (TB) remains one of deadly infectious diseases worldwide. Smoking habits are a significant factor that can increase TB transmission rates, as smokers are more susceptible to contracting TB than nonsmokers. Therefore, a control strategy that focused on minimizing TB transmission among smokers was essential. The control of TB transmission was evaluated based on the case detection rate. Undetected TB cases often resulted from economic challenges, low awareness, negative stigma toward TB patients, and health system delay (HSD). In this study, we developed a mathematical model that captured the dynamics of TB transmission specifically among smokers, incorporating the effects of case detection. Our innovative approach lied in the integration of smoking behavior as a key factor in TB transmission dynamics, which has been underexplored in previous models. We analyzed the existence and stability of the TB model equilibrium based on the basic reproduction number. Additionally, parameter sensitivity analysis was conducted to identify the most influential factors in the spread of the disease. Furthermore, this study investigated the effectiveness of various control strategies, including social distancing for smokers, TB screening in high-risk populations, and TB treatment in low-income communities. By employing the Pontryagin maximum principle, we solved optimal control problems to determine the most effective combination of interventions. Simulation results demonstrated that a targeted combination of control measures can effectively reduce the number of TB-infected individuals.

In contemporary society, proper waste management is a critical issue that needs to be addressed. Waste management encompasses the collection, transportation, segregation and disposal of waste material to minimize health risks and environment impact. Manual segregation, along with other methods of waste segregation, is often inefficient and time consuming. To address this challenge, numerous industries have embraced automation in waste sorting to expedite the process through advanced technological interventions. Therefore, the optimal functioning of the components of these automated systems is crucial for rapid and accurate segregation of waste. This work is oriented toward the study of a system which is used to segregation of waste and known as waste sorting robotic arm system (WSRAS). Author used Markov decision process, along with mathematical modeling, to evaluate the different performance measure of WSRAS. Sensitivity analysis have also been done to understand the contribution of different components failure in overall performance of WSRAS.

In this article, the dynamic behavior and solitary wave solutions of the Akbota equation were studied based on the analysis method of planar dynamic system. This method can not only analyze the dynamic behavior of a given equation, but also construct its solitary wave solution. Through traveling wave transformation, the Akbota equation can easily be transformed into an ordinary differential equation, and then into a two-dimensional dynamical system. By analyzing the two-dimensional dynamic system and its periodic disturbance system, planar phase portraits, three-dimensional phase portraits, Poincaré sections, and sensitivity analysis diagrams were drawn. Additionally, Lyapunov exponent portrait of a dynamical system with periodic disturbances was drawn using mathematical software. According to the maximum Lyapunov exponent portrait, it can be deduced whether the system is chaotic or stable. Solitary wave solutions of the Akbota equation are presented. Moreover, a visualization diagram and contour graphs of the solitary wave solutions are presented.

A nonautonomous mathematical model was presented to explore the complex dynamics of disease spread over time, incorporating a time-periodic transmission parameter and imperfections in quarantine, isolation and vaccination strategies. Through a detailed examination of threshold dynamics, it was revealed that the global dynamics of disease transmission are influenced by the basic reproduction number ($ \mathcal{R}_0 $), a critical threshold that determines extinction, persistence, and the presence of periodic solutions. It was shown that the disease-free equilibrium is globally asymptotically stable if $ \mathcal{R}_0 < 1 $, while the disease persists if $ \mathcal{R}_0 > 1 $. To support and validate our analytical results, the basic reproduction number and the dynamics of the disease were estimated by fitting monthly data from two Asian countries, namely Saudi Arabia and Pakistan. Furthermore, a sensitivity analysis of the time-averaged reproduction number ($ \langle \mathcal{R}_0 \rangle $) of the associated time-varying model showed a significant sensitivity to key parameters such as infection rates, quarantine rate, vaccine coverage rate, and recovery rates, supported by numerical simulations. These simulations validated theoretical findings and explored the impact of seasonal contact rate, imperfect quarantine, isolation, imperfect vaccination, and other parameters on the dynamics of measles transmission. The results showed that increasing the rate of immunization, improving vaccine management, and raising public awareness can reduce the incidence of the epidemic. The study highlighted the importance of understanding these patterns to prevent future periodic epidemics.

Tuberculosis (TB) remains a pressing global health concern, demanding urgent attention to mitigate its spread and impact. In this study, we present a rigorous mathematical model of TB transmission that incorporates early case detection and addresses the critical issue of treatment failure. Through the development of a system of nonlinear ordinary differential equations, we conduct comprehensive analyses to assess the dynamics of TB transmission and the efficacy of intervention strategies. Our findings underscore the urgent need for effective TB control measures. Mathematical analyses reveal that the model exhibits a TB-free equilibrium, which is globally asymptotically stable only if the control reproduction number falls below one. However, we identify a concerning phenomenon: the model demonstrates a forward bifurcation when the control reproduction number equals one, suggesting that the disease-free equilibrium loses its stability, while simultaneously, the stable unique endemic equilibrium begins to emerge. Moreover, sensitivity analysis highlights the complex interplay between case detection rates, treatment failure probabilities, and TB transmission dynamics. Contrary to expectations, increasing case detection rates and minimizing treatment failure probabilities may not consistently reduce the basic reproduction number or the size of the infected population. Instead, there exists a critical threshold for intervention effectiveness, beyond which TB transmission can be significantly curtailed. Biologically, this phenomenon may occur if there is no balance between case detection and treatment efforts. If treatment quality does not improve, then case detection will not have a significant impact, and in the worst case scenario, it can exacerbate the intervention’s negative effects. These findings underscore the urgency of implementing targeted intervention strategies to combat TB transmission effectively. Failure to meet the critical intervention threshold risks undermining TB elimination efforts and exacerbating the global TB burden. Through numerical simulations, we elucidate potential intervention scenarios necessary for achieving TB elimination goals in human populations. In conclusion, our study highlights the urgent imperative for coordinated action to control TB transmission effectively. By elucidating the dynamics of TB spread and intervention efficacy, we provide valuable insights to inform evidence-based policy decisions and accelerate progress towards TB elimination on a global scale.

Causal inference from observational data often rests on the unverifiable assumption of no unmeasured confounding. Recently, Tchetgen Tchetgen and colleagues have introduced proximal inference to leverage negative control outcomes and exposures as proxies to adjust for bias from unmeasured confounding. However, some of the key assumptions that proximal inference relies on are themselves empirically untestable. In addition, the impact of violations of proximal inference assumptions on the bias of effect estimates is not well understood. In this article, we derive bias formulas for proximal inference estimators under a linear structural equation model. These results are a first step toward sensitivity analysis and quantitative bias analysis of proximal inference estimators. While limited to a particular family of data generating processes, our results may offer some more general insight into the behavior of proximal inference estimators.

This work studies the behavior of electrical signals in resonant tunneling diodes through the application of the Lonngren wave equation. Utilizing the method of Lie symmetries, we have identified optimal systems and found symmetry reductions; we have also found soliton wave solutions by applying the tanh technique. The bifurcation and Galilean transformation are found to determine the model implications and convert the system into a planar dynamical system. In this experiment, the equilibrium state, sensitivity, and chaos are investigated and numerical simulations are conducted to show how the frequency and amplitude of alterations affect the system. Furthermore, local conservation rules are demonstrated in more detail to unveil the whole system of movements.

In a seminal article, Ding and VanderWeele proposed a method of constructing bounds for causal effects that has become widely recognized in causal inference. This method requires the analyst to provide guesses of certain “sensitivity parameters,” loosely defined as the maximal strength of association that an unmeasured confounder may have with the exposure and with the outcome. Ding and VanderWeele stated that their bounds are sharp, but without defining this term. Using a common definition of sharpness, Sjölander A. A note on a sensitivity analysis for unmeasured confounding, and the related E-value. J Causal Inference. 2020;8(1):229–48 showed that Ding and VanderWeele’s bounds are sharp in some regions of the sensitivity parameters, but are non-sharp in other regions. In this note, we follow up the work by Sjölander A. A note on a sensitivity analysis for unmeasured confounding, and the related E-value. J Causal Inference. 2020;8(1):229–48, by deriving bounds that are guaranteed to be sharp in all regions of Ding and VanderWeele’s sensitivity parameters. We illustrate the discrepancy between Ding and VanderWeele’s bounds and the sharp bounds with a real data example on vitamin D insufficiency and urine incontinence in pregnant women.

Given the prevailing circumstances surrounding the transmission of COVID-19, which has been classified as a worldwide epidemic by the World Health Organization, a sensitivity analysis was performed on the Protected-Susceptible-Infected-Treated- Protected- Susceptible ( ) epidemic model. The objective of this analysis was to identify the specific parameters associated with the basic reproduction number that contribute to the propagation of the COVID-19 epidemic in Najaf. The findings indicate that the sensitivity index of parameters exhibiting a positive sign is positively correlated with the extent of the epidemic's spread in Najaf. Conversely, parameters displaying a negative sign are inversely correlated with the spread of the epidemic. The analysis was conducted numerically using MATLAB to confirm the results of the study.

Our goal of this study is to prevent marijuana smoking in the human population. In this manuscript, an updated mathematical model was established by incorporating two additional compartments: The hospitalized class and the prisoner's class. The updated model was validated, and it was shown to be novel compared to the non-user, experimental, recreational, and addicted (NERA) users' model. This distinction was crucial as it was challenging to prevent marijuana usage without these realistic classes. The entire population was split into six primary groups, including these new classes: non-users, experimental, recreational, addicted, hospitalized, and prisoners' class. Additionally, control techniques for marijuana prevention in the population were addressed with the aid of sensitivity analysis. The important point at which we may have determined the preliminary transmission rate of marijuana smoking was the basic reproductive number R0. Utilizing MATLAB, the Runge-Kutta method of order four was employed for the numerical simulation of the updated model to investigate the impact of control measures on marijuana smoking prevention.

In this study, a dynamic model for typhoid fever incorporating protection against infection in the presence of saturated incidence rate is proposed. The existence and uniqueness solution is proved in order to ascertain the existence of the model. Stability analysis of endemic and disease free equilibrium was carried out to investigate the dynamic behavior of the transmission of the disease in a given population. Sensitivity analysis was also carried out to detect the impact of the parameters of the reproductive number and which parameters should focus as a control intervention. Numerical simulation of the model was carried out and the result is presented graphically, the result shows that an increase in the probability of the sources of protection and sociology factor dictate low disease prevalence in a population.

Tuberculosis has remained the principal cause of mortality worldwide, and one of the major sources of concern is drug-resistant TB. The increasing emergence of extensively drug-resistant and multidrug-resistant TB has further increased the TB epidemic. In this current work, we suggest a model to study the transmission of TB with extensively drug-resistant and multidrug-resistant compartments, incorporating chemoprophylaxis treatment. In the theoretical analysis, the concept of the next-generation matrix and the Jacobian method are applied to obtain a formula that states the reproductive number. The existence of endemic and disease-free equilibrium points was checked, and their stability has been analyzed using the Lyapunov method. The qualitative-based analysis indicated the local asymptotic stability of the disease-free-state for R0 1, whereas the endemic state is globally asymptotically stable if R0 1. Moreover, sensitivity analysis was carefully done using normalized forward sensitivity, and numerical simulation was carried out. Based on the results of numerical simulation and sensitivity analysis, chemoprophylaxis treatment was found to drastically minimize the progression of exposed individuals to infectious classes and also reduce the progression to extensively drug-resistant and multidrug-resistant classes, which decreases disease transmission.

In this article, the modified α equation is solved using the direct algebraic approach. As a result, numerous new and more generalized exact solutions for such equations have been found, taking into account the wide range of travelling structures. The rational, trigonometric, hyperbolic, and exponential functions with a couple of licentious parameters are thus included in these exact answers. Analytical solutions feature a variety of physical structures, which are visually studied to demonstrate their dynamic behavior in 2D and 3D. Considering the parameters, all feasible phase portraits are shown. Furthermore, we used numerical approaches to determine the nonlinear periodic structures of the mentioned model, and the data are graphically displayed. Additionally, we employed numerical approaches to determine the nonlinear conditions that contribute to the presented model, and the data are graphically displayed. After evaluating the influence of frequency following the application of an external periodic factor, sensitivity exploration is used to study quasi-periodic and chaotic behavior for several starting value problems. Furthermore, the function of physical characteristics is investigated using an external periodic force. Quasi-periodic and quasi-periodic-chaotic patterns are described with the inclusion of a perturbation term. The direct algebraic methodology would be used to derive the soliton solution of modified α equation, from which the Galilean transformation derives traveling wave solutions of the considered and a bifurcation behavior is reported. Analytical and numerical methods have been used to have the condition of the travelling wave phase transformation. The well-judged values of parameters are enhanced well with a graphically formal analysis of such specific solutions to illustrate their propagation. Then a planer dynamical system is introduced, and a bifurcation analysis is utilized to identify the bifurcation structures of the dynamical model’s nonlinear wave propagation solutions. Additionally, the periodic and quasi-periodic behavior of the discussed equation is analyzed using sensitivity analysis for a range of beginning values. To further comprehend the dynamical behaviors of the resultant solutions, a graphic analysis is conducted.

The Minimum Spanning Tree (MST) problem in networks focuses on finding efficient routes, with applications in transportation, logistics, telecommunications, and more. However, catastrophes can make these networks uncertain, requiring robust computational models for decision-making. This paper introduces an uncertainty theory-based model to analyze the stability of MSTs in uncertain networks. By incorporating reliability and risk variables, we assess the robustness of uncertain MSTs (UMSTs) and address the challenge of computing link tolerances, which define the range within which network links can vary without compromising MST optimality. This study proposes computational formulations to systematically calculate these tolerances, offering a more efficient alternative to traditional re-optimization methods.

Capturing the factors influencing yellow fever (YF) outbreaks is essential for effective public health interventions, especially in regions like Nigeria, where the disease poses significant health risks. This study explores the synergistic effects of active case detection (ACD) and early hospitalization on controlling YF transmission dynamics. We develop a dynamic model that integrates vaccination, active case detection, and hospitalization to enhance our understanding of disease spread and inform prevention strategies. Our methodology encompasses mechanistic dynamic modeling, optimal control analysis, parameter estimation, model fitting, and sensitivity analyses to study YF transmission dynamics, ensuring the robustness of control measures. We employ advanced mathematical techniques, including next-generation matrix methods, to accurately compute the reproduction number and assess outbreak transmissibility. Rigorous qualitative analysis of the model reveals two equilibria: disease-free and endemic, demonstrating global asymptotic stability and its impact on overall YF transmission dynamics, significantly affecting control and prevention mechanisms. Furthermore, through sensitivity analysis, we identify crucial parameters of the model that require urgent attention for more effective YF control. Moreover, our results highlight the critical roles of ACD and early hospitalization in reducing YF transmission. These insights provide a foundation for informed decision making and resource allocation in epidemic control efforts, ultimately contributing to the enhancement of public health strategies aimed at mitigating the impact of YF outbreaks.

The fourth-order nonlinear Boussinesq water wave equation, which describes the propagation of long waves in the intertidal zone, is investigated in this study. The exact wave patterns of the equation were computed using the tanh method. As stability decreased, soliton wave structures were derived using similarity transformations. Numerical simulations supported these findings. The tanh method introduced a Galilean modification, leading to the discovery of several new exact solutions. Subsequently, the fourth-order nonlinear Boussinesq wave equation was transformed into a planar dynamical system using the travelling wave transformation. The quasi-periodic, cyclical, and nonlinear behaviors of the analyzed equation were particularly examined. Numerical simulations revealed that varying the physical parameters impacts the system’s nonlinear behavior. Graphs represent all possible examples of phase portraits in terms of these parameters. Furthermore, the study was proven to be highly beneficial for addressing issues such as shock waves and highly active travelling wave processes. Sensitivity analysis theory and the Lyapunov exponent were employed, offering a wide variety of linear periodic and first-frequency periodic characteristics. Sensitivity analysis and multistability analysis of the Boussinesq water wave equation were thoroughly investigated.

This research paper attempts to describe the transmission dynamic of zoonotic visceral leishmaniasis with the aid of a mathematical model by considering the asymptomatic stages in humans and animals. The disease is endemic in several countries. Data used in the research are obtained from the literature while some are assumed based on the disease dynamic. The consideration of both asymptomatic and the symptomatic infected individuals is incorporated in both humans and animals (reservoir), as well as lines of treatment for the human population. It is found that the model has two fixed points; the VL-free fixed point and the VL-endemic fixed point. Stability analysis of the fixed points shows that the VL-free fixed point is globally asymptotically stable whenever the basic reproduction number is less than one and the VL-endemic fixed point is globally asymptotically stable whenever the basic reproduction number is greater than one. Sensitivity analysis is conducted for the parameters in the basic reproduction number, and the profile of each state variable is also depicted using the data obtained from the literature and those assumed. The transmission probability from infected sandflies to animals, transmission probability from infected animals to sandflies, per capita biting rate of sandflies of animals, and rate of transfer from symptomatic infected animals to the recovered class are among the most sensitive parameters that have the greatest influence on the basic reproduction number. Moreover, the value of the basic reproduction number is obtained to be 0.98951, which may require further study, as the margin between potential disease control and outbreak is thin.

Artificial intelligence (AI) stands out as a significant technological innovation, driving progress in diverse areas such as big data analysis, supply chain management, energy efficiency, sustainable development, etc. The present study investigates how AI could contribute to the sustainability of the healthcare supply chain (HSC) and managing medical needs. Medical organizations can boost the logistics of their tasks, reduce pharmaceutical trash, and strengthen revenue projections through the adoption of AI tools. This study aims to provide a structured evaluation of AI-driven solutions for enhancing healthcare supply chain robustness, especially under conditions of uncertainty and complex logistics demands. To determine the investment value of AI applications in HSC management, the current research adopted a revolutionary multi-criteria decision-making (MCDM) methodology tailored to the healthcare sector’s unique demands, including six critical factors. In light of these criteria, six highly technologically advanced AI-based solutions are examined. The implementation of a circular intuitionistic fuzzy set (CIFS) in the instance discussed provides a versatile and expressive way to describe vague and uncertain information. This study leverages the CIF topology to address data complexities and uncover the underlying structural features of a large dataset. At the outset, we adopted the LOPCOW approach, which includes logarithmic variation to assign weights to criteria, whereas the AROMAN method utilizes a powerful two-step normalization technique to rank alternatives, hence guaranteeing a trustworthy and accurate appraisal. A substantial degree of robustness was confirmed by the technique following a comparison of the operators as well as sensitivity testing.

In this research work, we developed a fractional-order model for the transmission dynamics of malaria, incorporating two control strategies: health education campaigns and the use of insecticides. The theoretical analysis of the model is presented, including the computation of disease-free equilibrium and basic reproduction number. We analyzed the stability of the proposed model using a well-formulated Lyapunov function. Furthermore, model parameter estimation was carried out using real data from malaria cases reported in Zimbabwe. We found that the fractional-order model provided a better fit to the real data compared to the classical integer-order model. Sensitivity analysis of the basic reproduction number was performed using computed partial rank correlation coefficients to assess the effect of each parameter on malaria transmission. Additionally, we conducted numerical simulations to evaluate the impact of memory effects on the spread of malaria. The simulation results indicated that the order of derivatives significantly influences the dynamics of malaria transmission. Moreover, we simulated the model to assess the effectiveness of the proposed control strategies. Overall, the interventions were found to have the potential to significantly reduce the spread of malaria within the population.

Background: Large scale international assessments depend on invariance of measurement across countries. An important consideration when observing cross-national differential item functioning (DIF) is whether the DIF actually reflects a source of bias, or might instead be a methodological artifact reflecting item response theory (IRT) model misspecification. Determining the validity of the source of DIF has implications for how it is handled in practice. Method: We demonstrate a form of sensitivity analysis that can point to model misspecification induced by item complexity as a possible cause of DIF, and show how such a cause of DIF might be accommodated through attempts to generalize the IRT model for the studied item(s) in psychometrically and psychologically plausible ways. Results: In both simulated illustrations and empirical data from TIMSS 2011 and TIMSS 2019 4th and 8th Grade Math and Science, we have found that using a form of proposed IRT model generalization can substantially reduce DIF when IRT model misspecification is at least a partial cause of the observed DIF. Conclusions: By demonstrating item complexity as a possible valid source of DIF and showing the effectiveness of the proposed approach, we recommend additional attention toward model generalizations as a means of addressing and/or understanding DIF. [ABSTRACT FROM AUTHOR]

Indirect disease transmission is modeled via a fractional-order discretetime Susceptible-Infected-Contaminant (SIC) model vaccination as a control strategy. Two control actions are considered, giving rise to two different models: the vaccine efficacy model and the vaccination impact model. In the first model, the effectiveness of the vaccine is analyzed by introducing a new parameter, while in the second model, the impact of the vaccine is studied incorporating a new variable into the model. Both models are studied giving population thresholds to ensure the eradication of the disease. In addition, a sensitivity analysis of the Basic Reproduction Number has been carried out with respect to the effectiveness of the vaccine, the fractional order, the vaccinated population rate and the exposure rate. This analysis has been undertaken to study its effect on the dynamics of the models. Finally, the obtained results are illustrated and discussed with a simulation example related to the evolution of the disease in a pig farm.

This study presented a glioma growth model that accounts for drug-sensitive and drug-resistant cells in response to chemotherapy and anti-angiogenic therapy. Chemotherapy induces mutations in drug-sensitive cells, leading to the emergence of drug-resistant cells and highlighting the benefits of combined therapy. Anti-angiogenic therapy can mitigate mutations by inducing angiogenic dormancy. We have identified two reproduction numbers associated with the non-cell and disease-free states. Numerical sensitivity analysis has highlighted influential parameters that control glioma growth dynamics, emphasizing the interactions between drug-sensitive and drug-resistant cells. To reduce glioma endemicity among sensitive cases, it was recommended to decrease chemotherapy expenditure, increase angiogenic dormancy, and adjust chemotherapy infusion rates. In addition, to combat resistance to glioma endemicity, enhancing angiogenic dormancy is crucial.

The occurrence of pests and diseases during agricultural production affects the quality and quantity of agricultural products. It is important to evaluate the impact of various factors on pests to achieve optimal results of integrated pest management (IPM) during its implementation. In this paper, we considered the transient and non-transient effects of chemical control on pests and the effects on natural enemies at different times, and developed a corresponding pest control model. Detailed studies and comparisons were conducted for spraying pesticides either more or less frequently as compared to strategies for releasing natural enemies. The threshold conditions for global asymptotic stabilization of the pest extinction period solution was obtained. Using two-parameter and sensitivity analysis techniques, the parameters affecting the variation of the threshold were discussed. By comparing these two pest control strategies, we found the existence of optimal application and release frequencies. Finally, in order to control pests below the economic threshold level, the state-dependent pest model was numerically investigated. The results show that the presence or absence of chemical control of pests can depend on the values taken for the parameters in the model. Based on this information, pest control experts can make decisions about the best spraying time and the best release rate.

In the context of this investigation, we introduce an innovative mathematical model designed to elucidate the intricate dynamics underlying the transmission of Anthroponotic Cutaneous Leishmania. This model offers a comprehensive exploration of the qualitative characteristics associated with the transmission process. Employing the next-generation method, we deduce the threshold value $ R_0 $ for this model. We rigorously explore both local and global stability conditions in the disease-free scenario, contingent upon $ R_0 $ being less than unity. Furthermore, we elucidate the global stability at the disease-free equilibrium point by leveraging the Castillo-Chavez method. In contrast, at the endemic equilibrium point, we establish conditions for local and global stability, when $ R_0 $ exceeds unity. To achieve global stability at the endemic equilibrium, we employ a geometric approach, a Lyapunov theory extension, incorporating a secondary additive compound matrix. Additionally, we conduct sensitivity analysis to assess the impact of various parameters on the threshold number. Employing center manifold theory, we delve into bifurcation analysis. Estimation of parameter values is carried out using least squares curve fitting techniques. Finally, we present a comprehensive discussion with graphical representation of key parameters in the concluding section of the paper.

Vaccination is widely acknowledged as an affordable and cost-effective approach to guard against infectious diseases. It is important to take vaccination rate, vaccine effectiveness, and vaccine-induced immune decline into account in epidemic dynamical modeling. In this paper, an epidemic dynamical model of vaccination is developed. This model provides a framework of the infectious disease transmission dynamics model through qualitative and quantitative analysis. The result shows that the system may have multiple equilibria. We used the next-generation operator approach to calculate the maximum spectral radius, that is, basic reproduction number $ {R_{vac}} $. Next, by dividing the model into infected and uninfected subjects, we can prove that the disease-free equilibrium is globally asymptotically stable when $ {R_{vac}} < 1 $, provided certain assumptions are satisfied. When $ {R_{vac}} > 1 $, there exists a unique endemic equilibrium. Using geometric methods, we calculate the second compound matrix and demonstrate the Lozinskii measure $ \bar q \leqslant 0 $, which is equivalent to the unique endemic equilibrium, which is globally asymptotically stable. Then, using center manifold theory, we justify the existence of forward bifurcation. As the vaccination rate decreases, the likelihood of forward bifurcation increases. We also theoretically show the presence of Hopf bifurcation. Then, we performed sensitivity analysis and found that increasing the vaccine effectiveness rate can curb the propagation of disease effectively. To examine the influence of vaccination on disease control, we chose the vaccination rate as the optimal vaccination control parameter, using the Pontryagin maximum principle, and we found that increasing vaccination rates reduces the number of infected individuals. Finally, we ran a numerical simulation to finalize the theoretical results.

Three models for the propagation of forest disease are revisited to include the effect of forest fires and disease spread. We study the global stability of the forest-disease model in the absence of forest fires and the spread of disease. When forest fires caused by grass cover are considered, we show that the equilibrium points are locally asymptotically stable. If both forest fires and the spread of disease exist in the second model, then Turing instability can occur. In this case, the system exhibits complex dynamic behavior. To determine the effect of fire on the forest disease model, we obtain the optimal control expression of the key parameter fire factor, and carry out sensitivity analysis. Finally, we use forest biomass data of some provinces in China from 2002 to 2018 for numerical simulation, and the results are in agreement with the theoretical analysis.

Cholera is an acute diarrhoeal illness that affects humanity globally, especially in areas where there is limited access to clean water and adequate sanitation. A Nigerian cholera outbreak from January 2021 to January 2022 resulted in many cases and deaths. A mathematical model that takes into consideration the challenges that affected effective implementation of control measures for this 2021 cholera outbreak is developed. Important epidemiological features of the model such as the basic reproduction number (R0), the disease-free equilibrium, and the endemic equilibrium are determined and analysed. The disease-free equilibrium is shown to be asymptotically stable provided R0 < 1. The model is shown to undergo forward bifurcation at R0 = 1 using the Centre Manifold Theorem. Sensitivity analysis is used to determine the parameters that have the highest influence on transmission. Fitting the model to data from the 2021 Nigerian cholera outbreak, important parameters of the model are estimated. The impact of control measures as well as challenges that affected the effective implementation of these control measures are considered.

This research was conducted to analyze and evaluate the feasibility of the bentonite mining business carried out by CV. Bentonit Ariyanto. The calculations in this research use Discounted Cash Flow (DCF). Discounted Cash Flow (DCF) is a cash flow calculation method that calculates the time value of money. Money invested in the present will have a different value in the future. From the calculation results using the Discounted Cash Flow method CV. BENTONIT ARIYANTO has a Net Present Value (NPV) of 2,864,612,232 > 0, Payback Period (PBP) 6 years 9 months < Age of Mine, Internal Rate of Return (IRR) 17.48% > MARR, Profitability Index (PI) 1, 95 > 1 and Sensitivity Analysis has a value when the selling price falls 5% and costs remain the same, the NPV value is 1,741,946,278, IRR 15.97%, PBP 9 years 1 month, PI 1.58. When the selling price falls 15% and costs remain the same, the NPV value is -503,385,631, IRR 10.78%, PBP 10 years 5 months, PI 0.83. When the selling price increases by 12.5% ​​from the current selling price and costs remain the same, the NPV value is 5,671,277,118, IRR 19.9%, PBP 4 years 3 months, and PI 2.89

Oncology research has focused extensively on estrogen hormones and their function in breast cancer proliferation. Mathematical modeling is essential for the analysis and simulation of breast cancers. This research presents a novel approach to examine the therapeutic and inhibitory effects of hormone and estrogen therapies on the onset of breast cancer. Our proposed mathematical model comprises a nonlinear coupled system of partial differential equations, capturing intricate interactions among estrogen, cytotoxic T lymphocytes, dormant cancer cells, and active cancer cells. The model's parameters are meticulously estimated through experimental studies, and we conduct a comprehensive global sensitivity analysis to assess the uncertainty of these parameter values. Remarkably, our findings underscore the pivotal role of hormone therapy in curtailing breast tumor growth by blocking estrogen's influence on cancer cells. Beyond this crucial insight, our proposed model offers an integrated framework to delve into the complexity of tumor progression and immune response under hormone therapy. We employ diverse experimental datasets encompassing gene expression profiles, spatial tumor morphology, and cellular interactions. Integrating multidimensional experimental data with mathematical models enhances our understanding of breast cancer dynamics and paves the way for personalized treatment strategies. Our study advances our comprehension of estrogen receptor-positive breast cancer and exemplifies a transformative approach that merges experimental data with cutting-edge mathematical modeling. This framework promises to illuminate the complexities of cancer progression and therapy, with broad implications for oncology.

Transfer learning has surfaced as a compelling technique in machine learning, enabling the transfer of knowledge across networks. This study evaluates the efficacy of ImageNet pretrained state-of-the-art networks, including DenseNet, ResNet, and VGG, in implementing transfer learning for prepruned models on compact datasets, such as Fashion MNIST, CIFAR10, and CIFAR100. The primary objective is to reduce the number of neurons while preserving high-level features. To this end, local sensitivity analysis is employed alongside p-norms and various reduction levels. This investigation discovers that VGG16, a network rich in parameters, displays resilience to high-level feature pruning. Conversely, the ResNet architectures reveal an interesting pattern of increased volatility. These observations assist in identifying an optimal combination of the norm and the reduction level for each network architecture, thus offering valuable directions for model-specific optimization. This study marks a significant advance in understanding and implementing effective pruning strategies across diverse network architectures, paving the way for future research and applications.

This study aims to develop a mathematical model for analyzing Lassa fever transmission dynamics and proposing effective control measures. The stability of the Lassa fever-free equilibrium point is examined and the model's accuracy is assessed using real-world data. Additionally, the parameter values and the basic reproduction number are estimated. A sensitivity analysis is also conducted, which identifies the key drivers influencing transmission dynamics. Moreover, the impact of model parameters on basic reproduction numbers is investigated. Multiple control methodologies including use of Ribavirin, implementing mobile health technology and incorporating natural predators are devised and analyzed using optimal control theory to curtail virus transmission.

The aim of this paper is to investigate the spread of the HIV/AIDS epidemic in China during 2008–2021. A new mathematical model is proposed to study the dynamics of HIV transmission with acute infection, fast asymptomatic infections, and slow asymptomatic infections. The basic reproduction number is obtained by the next-generation matrix method. A quantitative analysis of the model, including the local behavior, global behavior, and permanence, is performed. Numerical simulations are presented to enhance the results of these analyses. The behavior or the model's parameters are estimated from real data. A sensitivity analysis shows that the proportion of asymptomatic infections co-infected with other diseases significantly affects the basic reproduction number. We further analyze the impact of implementing single and multiple measure(s) in parallel with the epidemic. The study results conclude that multiple measures are more effective in controlling the spread of AIDS compared to just one. The HIV epidemic can be effectively curbed by reducing the contact rate between fast asymptomatic infected individuals and susceptible populations, increasing the early diagnosis and screening of HIV-infected individuals co-infected with other diseases, and treating co-infected patients promptly.

The degradation of products is an integral part of their life-cycle, often following predictable trajectories. However, sudden, unexpected events, termed ’shocks’, can substantially alter these degradation paths. Shocks can significantly influence the pace of degradation, leading to accelerated system failure. Moreover, they may initiate changes in degradation patterns, transitioning from linear to non-linear or random trajectories. To address this challenge, we present a novel multi-state reliability model for competing failure processes that account for degradation-shock dependencies by considering the state-varying degradation pattern. The degradation process is divided into s-states, with each state treated according to its pattern based on the time-transform Wiener process. The reliability function is derived based on soft failure caused by continuous degradation involving the s-states, the sudden increase in degradation caused by random shocks, and hard failure due to some shock processes. Additionally, we performed a sensitivity analysis to determine which parameters have the most significant impact on product reliability. Due to the complexity of the likelihood function, we adopted the ABC method to estimate the model parameters. A simulation study and a practical application with micro-electro-mechanical systems (MEMS) degradation results are used to demonstrate the efficiency and effectiveness of the proposed approach.

This paper investigates the explicit, accurate soliton and dynamic strategies in the resolution of the Wazwaz–Benjamin–Bona–Mahony (WBBM) equations. By exploiting the ensuing wave events, these equations find applications in fluid dynamics, ocean engineering, water wave mechanics, and scientific inquiry. The two main goals of the study are as follows: Firstly, using the dynamic perspective, examine the chaos, bifurcation, Lyapunov spectrum, Poincaré section, return map, power spectrum, sensitivity, fractal dimension, and other properties of the governing equation. Secondly, we use a generalized rational exponential function (GREF) technique to provide a large number of analytical solutions to nonlinear partial differential equations (NLPDEs) that have periodic, trigonometric, and hyperbolic properties. We examining the wave phenomena using 2D and 3D diagrams along with a projection of contour plots. Through the use of the computational program Mathematica, the research confirms the computed solutions to the WBBM equations.

Tuberculosis (TB) is an infectious disease transmitted through the respiratory system. China is one of the countries with a high burden of TB. Since 2004, an average of more than 800,000 cases of active TB has been reported each year in China. Analyzing the case data from 2004 to 2018, we found significant differences in TB incidence by age group. A model of TB is put forward to explore the effect of age heterogeneity on TB transmission. The nonlinear least squares method is used to obtain the key parameters in the model, and the basic reproduction number Rv = 0.8017 is calculated and the sensitivity analysis of Rv to the parameters is given. The simulation results show that reducing the number of new infections in the elderly population and increasing the recovery rate of elderly patients with the disease could significantly reduce the transmission of TB. Furthermore, the feasibility of achieving the goals of the World Health Organization (WHO) End TB Strategy in China is assessed, and we obtained that with existing TB control measures it will take another 30 years for China to reach the WHO goal to reduce 90% of the number of new cases by the year 2049. However, in theory it is feasible to reach the WHO strategic goal of ending TB by 2035 if the group contact rate in the elderly population can be reduced, though it is difficult to reduce the contact rate.

One of central bank regulations that has direct impact on the banking industry is loan benchmark interest rate. Banks use it as a reference rate to determine their loan interest rate. In this paper, we study the role of loan benchmark interest rate on banking loan dynamics. The model is in the form of a difference equation that follows a gradient adjustment process. We study the loan equilibrium's stability via bifurcation theory. It is found that the benchmark rate must be set between the flip and transcritical values. Some numerical simulations are performed to confirm the analytical result. The stochastic case of the benchmark rate is also studied. In addition, we perform numerical sensitivity analysis of the benchmark rate with the model's other parameters.

Strangles is one of the most prevalent horse diseases globally. The infected horses may be asymptomatic and can still carry the infectious pathogen after it recovers, which are named asymptomatic infected horses and long-term subclinical carriers, respectively. Based on these horses, this paper establishes a dynamical model to screen, measure, and model the spread of strangles. The basic reproduction number $ \mathcal{R}_0 $ is computed through a next generation matrix method. By constructing Lyapunov functions, we concluded that the disease-free equilibrium is globally asymptotically stable if $ \mathcal{R}_0 < 1 $, and the endemic equilibrium exits uniquely and is globally asymptotically stable if $ \mathcal{R}_0 > 1 $. For example, while studying a strangles outbreak of a horse farm in England in 2012, we computed an $ \mathcal{R}_0 = 0.8416 $ of this outbreak by data fitting. We further conducted a parameter sensitivity analysis of $ \mathcal{R}_0 $ and the final size by numerical simulations. The results show that the asymptomatic horses mainly influence the final size of this outbreak and that long-term carriers are connected to an increased recurrence of strangles. Moreover, in terms of the three control measures implemented to control strangles(i.e., vaccination, implementing screening regularly and isolating symptomatic horses), the result shows that screening is the most effective measurement, followed by vaccination and isolation, which can provide effective guidance for horse management.

The goal of this paper is to introduce a non-autonomous environmental transmission model for most respiratory and enteric infectious diseases to study the impact of periodic environmental changes on related infectious diseases. The transmission and decay rates of pathogens in the environment are set as periodic functions to summarize the influence of environmental fluctuations on diseases. The solutions of the model are qualitatively analyzed, and the equilibrium points and the reference criterion, $ R_0 $, for judging the infectivity of infectious diseases are deduced. The global stability of the disease-free equilibrium and the uniform persistence of the disease are proved by using the persistence theory. Common infectious diseases such as COVID-19, influenza, dysentery, pertussis and tuberculosis are selected to fit periodic and non-periodic models. Fitting experiments show that the periodic environmental model can respond to epidemic fluctuations more accurately than the non-periodic model. The periodic environment model is reasonable and applicable for seasonal infectious diseases. The response effects of the periodic and non-periodic models are basically the same for perennial infectious diseases. The periodic model can inform epidemiological trends in relevant emerging infectious diseases. Taking COVID-19 as an example, the sensitivity analysis results show that the virus-related parameters in the periodic model have the most significant influence on the system. It reminds us that, even late in the pandemic, we must focus on the viral load on the environment.

In the industrial sector, problems are often found in optimizing production results in order to obtain maximum profits. Pia home industry Mrs. Sandra has a problem in maximizing profits, namely finding solutions to produce pia with the optimal amount. The purpose of this study was to determine the amount of production and optimal profit obtained in the production of pia in the home industry using the branch and bound method and to determine the results of the sensitivity analysis to changes in production components. The results of the analysis show that using the branch and bound method, the home industry pia Mrs. Sandra gets an optimal profit of Rp. 2,078,557 per month by producing 1,666 pia chocolate, 1,041 pia temo, and 800 pia peanuts per month. The results of the sensitivity analysis show that profits will remain in optimal conditions if Mrs. Sandra's pia home industry follows the changes that occur in production components based on the upper bound and lower bound according to the output produced using Lingo 19.0 software

We present two methods for bounding the probabilities of benefit (a.k.a. the probability of necessity and sufficiency, i.e., the desired effect occurs if and only if exposed) and harm (i.e., the undesired effect occurs if and only if exposed) under unmeasured confounding. The first method computes the upper or lower bound of either probability as a function of the observed data distribution and two intuitive sensitivity parameters, which can then be presented to the analyst as a 2-D plot to assist in decision-making. The second method assumes the existence of a measured nondifferential proxy for the unmeasured confounder. Using this proxy, tighter bounds than the existing ones can be derived from just the observed data distribution.

Melanoma is considered one of the most aggressive types of cancer due to its high propensy for metastasis, which significantly reduces survival chances when detected late. Moreover, melanoma exhibits strong immunogenic characteristics, complicating its treatment, increasing the need to develop more effective techniques of therapy. In the field of oncology, mathematical modeling enables the analysis and distinction of the various mechanisms involved in tumor progression. This allows the analysis of numer- ous scenarios, which would be impractical experimentally. The main objective of this study is to develop a mathematical model that describes melanoma dynamics in the presence of Tumor-Associated Macrophages (TAM) and Chimeric Antigen Receptor (CAR) T-cell immunotherapy. The goal is to assess why this therapy often falls short in erradicating solid tumors like melanoma and to understand the role of TAM in this failure. This research encompasses stability analysis of the equilibrium points of the model, sensitivity analysis of its parameters, and the examination of numerical solutions. Our results showed that immunosuppression caused by TAM has a negative impact on the effectiveness of the dose and varying the cytotoxicity of CAR T-cells together with dose. Adjusting CAR T-cell cytotoxicity and treatment dosage may enhance tumor control, with the initial tumor burden playing a crucial role in treatment effectiveness.

Malaria is a disease caused by the parasite Plasmodium, transmitted by the bite of an infected female Anopheles. In general, five species of Plasmodium that can cause malaria. Of the five species, Plasmodium falciparum and Plasmodium vivax are two species of Plasmodium that can allow malaria superinfection in the human body. Typically, the popular intervention for malaria eradication is the use of fumigation to control the vector population and provide good medical services for malaria patients. Here in this article, we formulate a mathematical model based on a host-vector interaction. Our model considering two types of plasmodium in the infection process and the use of medical treatment and fumigation for the eradication program. Our analytical result succeeds in proving the existence of all equilibrium points and how their existence and local stability criteria depend not only on the control reproduction number but also in the invasive reproduction number. This invasive reproduction number represent how one plasmodium can dominate other plasmodium. Our sensitivity analysis shows that fumigation is the most influential parameter in determining all control reproduction numbers. Furthermore, we find that the order in which numerous intervention measures are taken will be very crucial to determine the level of success of our malaria eradication program.

The Aedes Aegypti mosquito is the primary vector that can transmit diseases to humans such as zika, dengue fever, chikungunya, and yellow fever. This mosquito species is controlled to reduce the frequency of its bites on humans. Several methods have been developed to control mosquito populations, ranging from natural insecticides to artificial ones. However, the impact of these insecticides leads to resistance. Wolbachia bacteria as a promising alternative in reducing the spread of viruses on humans due to free resistance. This work constructs a genetic population model in the form of differential equation system that describes mosquito population dynamics by involving random mating between mosquito populations with and without Wolbachia bacteria. The stability of the equilibrium was analyzed locally here. Numerical simulations and sensitivity analyzes are presented to confirm the analytical results and investigate the effect of the parameters involved on the model. The results show that the success of the expansion of Wolbachia-infected mosquitoes depends on the fitness level of the mosquito species. The more Wolbachia mosquitoes are released into nature, the more possibility this mosquito expansion will be successful.

Environmental science and pollution research has benefits around the globe. Human activity produces more garbage throughout the day as the world's population and lifestyles rise. Choosing a garbage disposal site (GDS) is crucial to effective disposal. In illuminated of the advancements in society, decision-makers concede a significant challenge for assessing an appropriate location for a garbage disposal site. This research used a multi-attribute decision-making (MADM) approach based on $ q $-rung orthopair hesitant fuzzy rough ($ q $-ROHFR) Einstein aggregation information for evaluating GDS selection schemes and providing decision-making (DM) support to select a suitable waste disposal site. In this study, first, q-ROHFR Einstein average aggregation operators are integrated. Some intriguing characteristics of the suggested operators, such as monotonicity, idempotence and boundedness were also explored. Then, a MADM technique was established using the novel concept of $ q $-ROHFR aggregation operators under Einstein t-norm and t-conorm. In order to help the decision makers (DMs) make a final choice, this technique aims to rank and choose an alternative from a collection of feasible alternatives, as well as to propose a solution based on the ranking of alternatives for a problem with conflicting criteria. The model's adaptability and validity are then demonstrated by an analysis and solution of a numerical issue involving garbage disposal plant site selection. We performed a the sensitivity analysis of the proposed aggregation operators to determine the outcomes of the decision-making procedure. To highlight the potential of our new method, we performed a comparison study using the novel extended TOPSIS and VIKOR schemes based on $ q $-ROHFR information. Furthermore, we compared the results with those existing in the literature. The findings demonstrate that this methodology has a larger range of information representation, more flexibility in the assessment environment, and improved consistency in evaluation results.

A transmission dynamics model with the logistic growth of cystic echinococcus in sheep was formulated and analyzed. The basic reproduction number was derived and the results showed that the global dynamical behaviors were determined by its value. The disease-free equilibrium is globally asymptotically stable when the value of the basic reproduction number is less than one; otherwise, there exists a unique endemic equilibrium and it is globally asymptotically stable. Sensitivity analysis and uncertainty analysis of the basic reproduction number were also performed to screen the important factors that influence the spread of cystic echinococcosis. Contour plots of the basic reproduction number versus these important factors are presented, too. The results showed that the higher the deworming rate of dogs, the lower the prevalence of echinococcosis in sheep and dogs. Similarly, the higher the slaughter rate of sheep, the lower the prevalence of echinococcosis in sheep and dogs. It also showed that the spread of echinococcosis has a close relationship with the maximum environmental capacity of sheep, and that they have a remarkable negative correlation. This reminds us that the risk of cystic echinococcosis may be underestimated if we ignore the increasing number of sheep in reality.

Media coverage can greatly impact the spread of infectious diseases. Taking into consideration the impacts of media coverage, we propose an SEIR model with a media coverage mediated nonlinear infection force. For this novel disease model, we identify the basic reproduction number using the next generation matrix method and establish the global threshold results: If the basic reproduction number $ \mathcal{R}_{0} < 1 $, then the disease-free equilibrium $ P_{0} $ is stable, and the disease dies out. If $ \mathcal{R}_{0} > 1 $, then the endemic equilibrium $ P^{*} $ is stable, and the disease persists. Sensitivity analysis indicates that the basic reproduction number $ \mathcal{R}_{0} $ is most sensitive to the population recruitment rate $ \Lambda $ and the disease transmission rate $ \beta _{1} $.