Search Results (321)

The coffee berry borer (Hypothenemus hampei) is the primary pest of coffee crops worldwide. Sustainable management strategies increasingly rely on the integration of biological control and interventions activated by population thresholds. In this work, a comparative framework based on dynamical systems is presented, integrating three complementary mathematical models to analyze different management strategies for the coffee berry borer. First, a biologically structured three-dimensional model describes the interaction between adult and immature borers and predatory ants. Second, a two-dimensional formulation allows the maximum per capita consumption rate of the predator to be studied as a bifurcation parameter, identifying critical parameter values that delimit regions of coexistence or effective pest control. Finally, a piecewise-smooth dynamical system incorporates ethological control activated when infestation exceeds a predefined threshold, whose effectiveness depends on the capture intensity associated with the traps. Using stability theory, bifurcation analysis, and techniques from piecewise-smooth dynamical systems, parametric regions associated with persistence, coexistence, or significant pest reduction are characterized. The results show that biological control alone may be insufficient if a predation threshold is not exceeded, whereas its combination with early threshold-based interventions considerably enlarges the dynamical regions favorable to producers. This study provides a dynamical interpretation of the agricultural concept of intervention threshold and offers a quantitative framework to strengthen integrated management and the sustainability of coffee production. Full article

Understanding the effects of light on the body at different times of the 24 h solar day is a topic of increasing interest. In this paper, we use a mathematical model from the literature to simulate what would be expected of the human circadian clock on different light schedules. We first reproduce an influential experiment which found eBooks, when compared to a paper book, delayed sleep by roughly 10 min and melatonin onset by 1.5 h. The model is able to match the delay in sleep onset but struggles to reproduce the melatonin phase delay. However, certain initial conditions and parameters are capable of phase shifts consistent with the original study’s magnitude, suggesting that the original study’s finding may have been influenced by the pre-study entrainment or variability among the participants. We next simulate the same protocol under higher daytime light levels (increasing baseline illumination from 90 to 500 lux) and find that brighter daytime exposure reduces both sleep onset latency and the variability in phase delay attributable to evening eBook light. Finally, we explore how the timing of a bright light pulse during the day changes outcomes, such as sleep onset and circadian amplitude, and how these effects interact with light during the other hours of the 24 h day. Together, these modeling results suggest robust daytime light exposure confers resilience against the circadian-disruptive effects of evening light, generating testable predictions regarding the timing and intensity of beneficial light interventions for maintaining circadian alignment. Full article

Alzheimer’s disease (AD) develops as a progressive dementia condition through the step-by-step breakdown of nerve cells. Neurodegeneration in this context primarily results from metal ions, including copper, iron, zinc, and aluminum, building up in the system. The aggregation of amyloid-beta (Aβ) peptides and oxidative stress generation stem from metal ion involvement acting as defining characteristics of Alzheimer’s disease pathology. We developed a comprehensive mathematical model based on 24 coupled ordinary differential equations (ODEs) to represent the interactions between metal ions, Aβ peptides, reactive oxygen species (ROS), antioxidant defenses, and tau protein phosphorylation. The mathematical model monitors how metal ion concentrations change over time and examines their competitive binding effects, which trigger a series of reactions, resulting in oxidative stress and subsequent tau protein damage. The model uses analytical and numerical mathematical methods to expose nonlinear behaviors and threshold effects while offering mechanistic insights into the course of disease development. This model functions as a quantitative framework for assessing how therapeutic interventions that target metal dyshomeostasis and oxidative stress can potentially affect outcomes. Full article

In this paper, we present a mathematical analysis of within-host CHIKV dynamics by developing and studying a novel delay differential equation model that incorporates persistent infected monocytes, discrete time delays, and an antibody-mediated humoral immune response. The model includes five compartments: susceptible monocytes, persistent infected monocytes, actively infected monocytes, CHIKV pathogens, and neutralizing antibodies. To reflect key biological latencies, we introduce four distinct discrete delays accounting for the periods between viral entry and the emergence of infected cell populations, intracellular virion production, and antibody activation. We analyze the model, establishing the positivity, boundedness, and invariance of solutions, and derive the basic reproduction number ${\mathcal{R}}_0$ via the next-generation matrix method. Using Lyapunov functions and LaSalle’s Invariance Principle, we prove a threshold dynamic: the infection-free equilibrium is globally asymptotically stable (GAS) when ${\mathcal{R}}_0\le 1$, while a unique endemic equilibrium is GAS when ${\mathcal{R}}_0>1$. Numerical simulations validate the analytical results and illustrate threshold behavior. A detailed local sensitivity analysis of ${\mathcal{R}}_0$ identifies the most influential parameters, offering theoretical insights into potential intervention strategies. We further investigate the effects of antiviral therapy as a theoretical intervention, deriving a treatment-dependent reproduction number and the critical drug efficacy required for eradication, and explore how the intracellular production delay can itself serve as a critical threshold for infection clearance. The study provides a rigorous theoretical framework that highlights the roles of latency, immune response, and biological delays in CHIKV pathogenesis and offers qualitative insights that may inform future experimental and treatment design studies. Full article

Brain–Computer Interfaces (BCIs) have increasingly been explored as tools for monitoring and modulating cognitive processes relevant to learning. However, their application to learning disorders, and especially to mathematical learning difficulties such as dyscalculia and ageometria, remains conceptually promising but empirically underdeveloped. The present study offers a scoping review with structured narrative synthesis of recent empirical research on BCI-based interventions in learning disorder populations, with particular attention paid to their possible translational relevance for mathematical learning. Following PRISMA-ScR principles and a Population–Concept–Context framework, studies published between 2020 and 2025 were identified through database searches in Scopus, IEEE Xplore, and PubMed. A total of 30 studies met the inclusion criteria. All eligible studies focused on Attention-Deficit/Hyperactivity Disorder (ADHD), while no eligible BCI intervention studies were found for dyscalculia or ageometria. The reviewed literature was dominated by EEG-based neurofeedback interventions. To move beyond descriptive summary, the included studies were organized using a structured analytical framework based on intervention modality, primary cognitive target, methodological robustness, and translational proximity to mathematical learning disorders. Across the evidence base, the most consistent findings concerned attention regulation and executive function outcomes, whereas academic and mathematics-related outcomes were sparse and methodologically less developed. Although several studies suggested improvements in domain-general cognitive mechanisms relevant to mathematical learning, the absence of direct evidence in dyscalculia and ageometria prevents confirmatory conclusions. The review therefore identifies both the promise and the limits of current BCI applications in learning disorder contexts and argues that future research should prioritize theory-driven, disorder-specific trials targeting numeracy, visuospatial reasoning, and executive processes in mathematical learning disabilities. Although current findings suggest promising cognitive and educational potential, these technologies are not yet ready for routine implementation in standard classroom environments without further validation, teacher training, ethical safeguards, and cost-effective deployment models. Full article

Mathematics is a diverse discipline that requires a variety of cognitive abilities and presents varying levels of difficulty. Understanding how different cognitive profiles relate to specific patterns of mathematical performance is important for developing effective educational interventions. This study extends our previous research, in which we identified subgroups of children with mathematical difficulties based on their cognitive abilities. We examined 146 Israeli elementary school children in grades 3 and 4, classified into four subgroups: Reading Accuracy Difficulties (RAD), Mild Mathematical Difficulties (MMD), Non-Verbal Reasoning Difficulties (NVRD), and Typically Developing children (TD). Participants were assessed on arithmetic facts, computational fluency, procedural skills, estimation, and numeration. We observed varied performance patterns among subgroups. The RAD group showed the most severe impairments across all mathematical domains, along with reading comorbidity and cognitive difficulties. The MMD group, which maintained intact cognitive skills, faced notable challenges in computation, performing significantly below the TD group but better than the RAD group. The NVRD group, despite limitations in nonverbal reasoning, outperformed other difficulty groups on fact retrieval and estimation. Performance on multiplication and division tasks consistently followed a hierarchical pattern across all difficulty groups, with the RAD group facing the greatest challenges. These findings demonstrate that mathematical difficulties vary across cognitive profiles and that distinguishing between profiles through targeted assessment enables the development of differentiated interventions tailored to each learner’s specific cognitive profile. Full article

Measles remains a significant public health threat despite widespread vaccination, with recent resurgences driven by vaccine hesitancy and coverage gaps. Existing mathematical models often fail to capture the substantial temporal heterogeneity in incubation periods, vaccine-induced protection, and recovery processes that characterize measles transmission. We develop and analyze an SVEIR epidemic model incorporating four independent distributed time delays with exponential survival factors, capturing the realistic variability in these epidemiological processes. The model features compartment-specific mortality rates, disease-induced mortality, and imperfect vaccination with failure probability $\theta$. Using next-generation matrix methods adapted for delay kernels, we derive the delay-dependent reproduction number ${\mathcal{R}}_0^d$ and prove, via systematic construction of Volterra-type Lyapunov functionals, that it constitutes a sharp threshold: the disease-free equilibrium is globally asymptotically stable when ${\mathcal{R}}_0^d\le 1$, while a unique endemic equilibrium emerges and is globally stable when ${\mathcal{R}}_0^d>1$. Normalized forward sensitivity analysis reveals that the transmission rate $\beta$ and recruitment rate $\Lambda$ exhibit maximal positive elasticity, while the vaccination rate p, vaccine failure probability $\theta$, and incubation delay ${\tau }_3$ possess the largest negative elasticities. Critically, ${\tau }_3$ exerts exponential influence via $e^{-n_3{\tau }_3}$, making interventions that delay infectiousness—such as post-exposure prophylaxis—unusually potent. We derive an explicit expression for the critical delay ${\tau }_3^{\mathrm{cr}}$ at which ${\mathcal{R}}_0^d=1$, demonstrating that prolonging the effective incubation period sufficiently can shift the system from endemic persistence to extinction. Numerical simulations using Dirac delta kernels confirm all theoretical predictions. These findings provide three actionable insights for public health: (1) maintaining high vaccination coverage among new birth cohorts remains paramount; (2) improving vaccine quality (reducing $\theta$) yields substantial returns; and (3) the incubation delay represents a quantifiable, measurable target for evaluating the population-level impact of time-sensitive interventions. The framework is broadly applicable to infectious diseases characterized by significant temporal heterogeneity. Full article

Given the constraints inherent to island tourism resources, optimizing their allocation and utilization scientifically and efficiently has emerged as a critical challenge for both academic inquiry and policy-making. This study investigates pathways to enhance island tourism sustainability through the development of mathematical models quantifying tourism intensity, efficiency, and resource abundance, utilizing multi-source heterogeneous data on tourism resources in Hainan from 2012 to 2022. The study reveals that: (1) The spatial structure of tourism development progressed from an initial “north–south dual-core driven, fragmented in the west” pattern, through an intermediate “north–south dual-core driven, fragmented in the east” phase, and ultimately evolved into a “north–south dual-core driven, east–west isolated” configuration. (2) Spatiotemporal evolution of Hainan Island’s tourism industry is driven by a combination of policy interventions, natural endowments, transport infrastructure, economic foundations and population size. (3) Tourism economic effects exhibit marked regional heterogeneity across Hainan. Eastern regions are strongly influenced by per capita tourism income and hotel density, whereas northern areas depend more on the tertiary industry share; significant spatial spillover effects are also observed. (4) Spatial econometric modeling further indicates that influential factors do not uniformly exert positive effects on the tourism sector and its subsystems, with indirect effects exceeding direct effects by approximately 22.41 times. Although this research underscores the importance of human–environment interactions, it does not quantify the specific ecological consequences of tourism development. Future policy should integrate an ecological footprint model within a coordinated “tourism–ecology–protection” framework to balance economic and ecological goals, while also accounting for external shocks affecting the tourism economy. Full article

This study develops an integrated mathematical model to investigate the interaction between tuberculosis (TB) transmission and childhood stunting, which is aligned with the United Nations Sustainable Development Goals (SDG 3). The population is structured into two age groups (0–5 years and ≥5 years), with stunting explicitly incorporated into the pediatric population to capture its potential influence on TB dynamics. The model is formulated as a system of ordinary differential equations and analyzed using equilibrium and stability analysis, with the basic reproduction number, $R_0$. The disease-free equilibrium is locally asymptotically stable when $R_0<1$, while an endemic equilibrium exists when $R_0>1$. Sensitivity analysis indicates that the transmission rate ($\beta$), progression rate from latent to active infection ($\sigma$), and recovery rate ($\gamma$) are the most influential parameters affecting $R_0$. These parameters are therefore selected as control variables in an optimal control framework to design effective intervention strategies. Numerical simulations show that the combined control strategy significantly reduces TB transmission, resulting in a reduction of more than $80\%$ in active TB cases within a relatively short intervention period. The results suggest that integrated interventions targeting transmission, disease progression, and recovery are substantially more effective than single-measure strategies. This study provides a quantitative framework to support integrated public health policies addressing TB and childhood stunting simultaneously. Full article

This study presents a comparative analysis of classroom engagement effects on the academic achievement of senior secondary school physics students, focusing on the replication of prior research and contrasting the impacts of guided and minimally guided constructivist instructional approaches. Drawing on established frameworks of inquiry-based instruction, particularly Cognitively Guided Instruction (CGIS) and Cubing Instruction (CIS), the research investigates their relative efficacy in enhancing student learning outcomes. The clustered quasi-experimental pretest–posttest design, involving the Cognitively Guided Instructional Strategy (CGIS) and the Cubing Instructional Strategy (CIS), was adopted by the study. The intact classroom groups of schools purposively selected participated in the study. An achievement test was administered before and after instruction, and the Analysis of Covariance (ANCOVA) and t-tests were used to determine the effects of the intervention while controlling for baseline achievement and mathematical ability. The findings show that the treatment had a significant effect on the students’ achievement (p = 0.030). The t-test result demonstrated that students exposed to the CGIS recorded higher posttest mean scores than those in the CIS group. These outcomes suggests that guided inquiry may offer pedagogical advantages in supporting classroom and conceptual learning. However, the evidence should be cautiously interpreted. The study contributes to the literature as a conceptual replication by providing evidence regarding the effects of guided and minimally guided constructivist approaches in a different instructional setting. The outcomes underscore the importance of balancing instructional guidance and learner autonomy in physics classrooms, as well as the need for further research involving larger samples and diverse contexts to strengthen causal inference. Full article

Numerous studies have shown that overweight and obesity significantly increase the risk of severe illnesses, including type 2 diabetes, hypertension, and knee osteoarthritis. This study aims to develop a generalized mathematical model to manage the growing prevalence of overweight and obesity. We first demonstrate that the model’s solution remains positive and bounded under specific conditions. To determine optimal intervention strategies, we apply Pontryagin’s minimum principle (PMP) to establish necessary optimality conditions. The Forward–Backward Sweeping Method (FBSM) is then used to obtain numerically optimal controls and to demonstrate their effect over a fixed time interval. The results indicate that the proposed approach effectively reduces overweight and obesity while ensuring cost-effectiveness. Full article

The future of innovation and economic growth depends on our ability to nurture the next generation of scientists. The global shortage of qualified STEM (Science, Technology, engineering, Mathematics) teachers has led many countries to expedite the transition of subject-matter experts from industry and academia into teaching roles. These second-career science student teachers typically participate in accelerated training programs designed to address urgent shortages. This study addresses a gap in the literature regarding effective pedagogical interventions for career-changing professionals in STEM fields, focusing on the experience and transformation of second-career science student teachers. This qualitative case study explores how a Challenge-Based Learning (CBL) course fosters the development of pedagogical competences via developing an instructional unit collaboratively, among five second-career science student teachers enrolled in an accelerated teacher education program. Drawing on data collected through instructors’ field notes, iterative work-in-progress lesson drafts, and reflective final papers, the study employs qualitative content analysis to trace changes in participants’ instructional approaches and professional identity. Findings reveal that engagement with the CBL framework promoted a significant shift from teacher-centered to learner-centered instruction, as participants increasingly integrated collaborative learning, inquiry-based activities, and reflective practices into their lesson planning and classroom teaching. The iterative nature of CBL, which emphasizes real-world problem-solving and structured opportunities for reflection and peer feedback, was instrumental in supporting participants’ adaptive expertise and confidence as novice teachers. Moreover, the course experience contributed to the emergence of a professional teaching identity, with participants reporting greater self-efficacy, a stronger sense of belonging to the teaching community, and increased motivation to persist in the profession. The results underscore the potential of integrating CBL and learning sciences principles into accelerated teacher preparation programs to enhance both cognitive and affective dimensions of teacher development. Full article

Despite consensus in the mathematics education literature regarding the mutually dependent components of math proficiency, as well as the importance of their development, most elementary-aged students in the United States demonstrate a lack of proficiency in math according to national assessment data. Whole number knowledge, which includes skills in computation and word-problem solving, is understood to be a critical foundation for the development of later math skills. This study used a multiple-baseline experimental design to evaluate the impacts of an evidence-based mathematics intervention, Accelerating Mathematics Performance with Practice Strategies (AMPPS), on third- through fifth-grade students’ skills with complex computation, as well as on their word-problem-solving performance. Furthermore, we evaluated effects on students’ math self-concept. Five students identified to have difficulties in math received AMPPS in a one-on-one, in-person format. The results of the study were mixed. For example, when using visual analyses as our primary analytic method, these analyses did not show robust intervention effects on students’ computation skills but did show at least some improvement for most students’ word-problem-solving skills. Additionally, supplemental analyses comparing student growth to national and school-based norms suggested that all participants seemed to benefit from the intervention, but these analyses were not intended to examine experimental causality. Despite study limitations and a lower than optimal number of AMPPS sessions (dosage) provided to students, the present study offers several directions for future research, as well as possible implications for practitioners regarding intervention selection, intensity, and evaluation. The findings will also be discussed in the context of conducting systematic replication studies, which are essential for understanding the generality of a given phenomenon (e.g., an effect of a school-based intervention) across a wide range of situations and conditions. Full article

The moderation of intervention effects by intelligence and prior knowledge deserves further investigation, because they inform how to design and implement interventions. This study analyzed the moderation of the effectiveness of a computer-based mathematics intervention in 10 primary school students with low mathematics performance and low-to-average intelligence in an ABAB-single-case research design. Prior knowledge and intelligence were assessed before the intervention. The computer-based intervention trained basic numerical skills. Visual inspection of the learning trajectories revealed a broad heterogeneity of effectiveness of the intervention. A hierarchical piecewise regression analysis across all students revealed a significant negative moderation of the intervention effectiveness through intelligence. Whereas prior knowledge did not have a moderating influence, children with higher intelligence showed slower learning rates during the intervention in this specific low-performing sample. One reason for the negative moderation of the intervention effects could be that the intervention trained strategies and skills that more intelligent students had already developed. Full article

Background: Tuberculosis remains a major global public health challenge. Mathematical models are essential for strategic planning and evaluation of tuberculosis control programs, while addressing socioeconomic risk factors has proven key to accelerating incidence declines. Therefore, this study quantitatively assesses the impact of socioeconomic interventions on tuberculosis incidence in Kazakhstan. Methods: A modified SIR compartmental model was developed in Python 3.12 to simulate tuberculosis transmission dynamics. Parameters were calibrated using the Nelder–Mead simplex algorithm, and predictive performance was evaluated via hold-out validation. Scenario-based projections were generated to explore the impact of socioeconomic improvements on future tuberculosis incidence. Results: The calibrated SIR model demonstrated strong predictive accuracy, achieving a mean absolute percentage error of 2.3%. The sensitivity analysis revealed that the model is robust to moderate socioeconomic perturbations, with healthcare funding and unemployment rate as the primary uncertainty drivers. Scenario simulations showed that enhanced financial assistance for tuberculosis patients produced the largest effect beyond baseline. Optimization results indicate that 7.4% rise in GDP per capita, 10.2% increase in healthcare funding, 23.1% and 19.1% reductions in poverty and unemployment rates, and 40.2% growth in tuberculosis patient financial support relative to 2024 are sufficient to achieve the WHO’s End TB Strategy 2030 target. Conclusions: The model offers a valuable tool for tuberculosis forecasting and intervention evaluation, highlighting the synergistic role of socioeconomic measures in achieving global elimination goals. Full article