Mathematical Biosciences and Engineering最新文献

Traffic sign recognition is crucial not only for autonomous vehicles and traffic safety research but also for multimedia processing and computer vision tasks. However, traffic sign recognition faces several challenges, such as high intraclass variability and interclass similarity in visual features and background complexity. We propose a novel invariant cue-aware feature concentration transformer (TTSNet) to effectively address these challenges. TTSNet aims to learn the invariant and core information of traffic signs. To this end, we introduce three new modules to learn the features of traffic signs: attention-based internal scale feature interaction (DLFL), cross-scale cross-space feature modulation (SSFM), and eliminating spatial and information redundancy (ESIR) modules. The DLFL module extracts invariant cues from traffic signs through feature selection based on discriminative values. The SSFM-Fusion module aggregates multi-scale information from traffic sign images by concatenating multi-layer features. The ESIR module improves feature representation by eliminating spatial and channel information redundancy. Extensive experiments showed that TTSNet achieves state-of-the-art performance on the T100K (89.1%) and CTSDB (89.97%) datasets.

This study presents, as a proof-of-concept, a mathematical model describing the transmission dynamics of cystic echinococcosis. This neglected zoonosis is caused by the larval stage of Echinococcus granulosus s.l. involving dogs and sheep as definitive hosts and sheep as intermediate hosts. The model incorporates the dual role of humans as final hosts and as active participants in the parasite's transmission cycle through practices such as feeding dogs with infected viscera. A system of nine ordinary differential equations represents human subpopulations (children and adults) and the concentration of viable parasite eggs. The basic reproductive number ($ R_0 $) was computed via the next-generation matrix approach, and bifurcation analysis indicated a forward bifurcation at $ R_{0} = 1, $ confirming that $ R_{0} < 1 $ ensures disease control. Global sensitivity analysis using Sobol indices identified the infestation rate ($ beta $) and adult transmission rate ($ beta_{AG} $) as the most influential parameters, explaining 35.9% and 29.9% of $ R_0 $ variance, respectively. These findings highlight that interventions reducing $ beta $ and $ beta_{AG} $ may effectively decrease human infection rates.

Open-loop optimal control applied to epidemic outbreaks is a valuable tool to develop control principles and inform future preparedness guidelines. A drawback of this approach is its assumption of complete knowledge of both transmission dynamics and the effects of policy measures. As a result, such methods lack responsiveness to real-time conditions, since they do not integrate feedback from the evolving epidemic state. Overcoming this requires a closed-loop approach. We propose a novel closed-loop method for real-time social distancing responses using a general Reinforcement Learning (RL)-based decision-support framework. It enables adaptive management of social distancing policies during an epidemic, thereby balancing direct health costs (e.g., hospitalizations, deaths) with indirect (economic, social, psychological) costs from prolonged interventions. The framework builds on and compares with a COVID-19 model that was previously used for open-loop assessments, thereby capturing key disease characteristics like asymptomatic transmission, healthcare saturation, and quarantine. We test the framework by evaluating optimal real-time responses for a severe outbreak under varying priorities of indirect costs by public authorities. The full spectrum of policy strategies-elimination, suppression, and mitigation-emerges depending on the cost prioritization as a result of closed-loop adaptability. The framework supports timely, informed decisions by governments and health authorities during current or future pandemics.

We developed a unified analytical framework for the global dynamics of discrete-time susceptible infectious susceptible (SIS) epidemic models with nonlinear recruitment. Emphasis was placed on demographic feedback through Beverton-Holt and Ricker-type recruitment, which regulates host population size and thereby shapes transmission and long-term persistence (Persistence allows population densities to approach zero asymptotically, wheras uniform persistence requires them to remain bounded away from zero). Under minimal assumptions, we reduced non-autonomous systems to appropriately defined autonomous limiting systems and used this reduction to obtain a complete global threshold characterization: When the basic reproduction number $ R_{0} > 1 $, the endemic equilibrium existed and was globally asymptotically stable; when $ R_{0}le 1 $, solutions converged to the disease-free state. The approach extended to periodically forced SIS models, which showed that the threshold and stability conclusions persisted in the periodic non-autonomous setting. The results unified and strengthened prior work and clarify how recruitment dynamics govern persistence in discrete-time epidemic systems.

This work investigated the combined effects of intraocular pressure (IOP) and blood pressure (BP) on retinal hemodynamics and glaucoma progression using a novel, physiology-based digital twin for ocular hemodynamics (DT-OH). The DT-OH integrates a mathematical model of ocular physiology with machine learning to simulate retinal blood flow dynamics based on individualized IOP and BP inputs. The DT-OH was applied to clinical data from the Indianapolis Glaucoma Progression Study (IGPS) to characterize how IOP and BP jointly influence retinal hemodynamics and their association with glaucoma progression. The DT-OH identified three distinct hemodynamic profiles based on the combined effects of IOP and BP. Membership in one specific profile at baseline was associated with a significantly higher risk of glaucoma progression. These profiles reflect distinct patterns of ocular blood flow regulation and provide physiological insight into the interplay between systemic and ocular factors in glaucoma. These findings enhance our understanding of glaucoma pathophysiology and support the development of personalized risk assessment tools that account for both IOP and BP.

We revisit the problem of minimizing the epidemic final size in the SIR model through social distancing of a bounded intensity. In the existing literature, this problem was considered imposing a priori interval structure on the time period when interventions are enforced. We show that the support of the optimal control is still a single time interval when considering the more general class of controls with an $ L^1 $ constraint on the confinement effort that reduces the infection rate. There is thus no benefit in splitting interventions on several disjoint time periods. However, if the infection rate is known beforehand to change with time once from one value to another one, then we show that the optimal solution may consist in splitting the interventions in at most two disjoint time periods.

Seasonal infectious diseases like influenza pose a recurrent challenge to public health. While compartmental models, such as the susceptible-infectious-recovered-susceptible (SIRS) framework, are standard tools, representing the time-varying transmission rate, $ beta(t) $, in an interpretable yet effective manner remains a key challenge. Existing established alternative methods for modeling seasonality use sinusoidal forcing functions, flexible splines, etc. In this paper, we propose and apply a modular approach where $ beta(t) $ is defined using distinct, epidemiologically intuitive seasonal rates, with smooth transitions between them. To begin, we develop this framework as a theoretical tool, demonstrating its capacity to generate realistic, recurring seasonal outbreaks under plausible parameter assumptions. We then calibrate and assess this model against real-world, monthly laboratory-confirmed influenza surveillance data from Ontario, Canada, for the pre-pandemic period of 2014-2019. A systematic optimization using a coarse grid search followed by stochastic refinement calibrates the model to the observed data. The calibrated model, featuring a mean immunity duration of approximately 235 days, achieves a strong fit with the historical case data (Pearson correlation $ r = 0.80 $). Our results demonstrate that this modular arithmetic-based framework is a practical and effective tool for modeling real-world influenza dynamics, successfully bridging the gap between theory and empirical surveillance.

Given the complexity, unknown causes, and lack of effective treatments for Alzheimer's disease (AD), mathematical modeling offers a valuable approach to its understanding. Models, once validated, offer a powerful tool to test medical hypotheses that are otherwise difficult to directly verify. Here, our focus is to elucidate the spread of misfolded $ tau $ protein, a critical hallmark of AD alongside A$ beta $ protein, while taking the synergistic interaction between the two proteins into account. We consider distinct modeling choices, all employing network frameworks for protein evolution, differentiated by their network architecture and diffusion operators. By carefully comparing these models against clinical $ tau $ concentration data, gathered through advanced multimodal analysis techniques, we show that certain models replicate better the protein's dynamics. This investigation underscores a crucial insight: when modeling complex pathologies, the precision with which the mathematical framework is chosen is crucial, especially when validation against clinical data is considered decisive.

Acidosis in tumors arises from reprogrammed metabolism and compromised vasculature, creating a harsh, acidic microenvironment that drives the evolutionary selection of acid-resistant cell phenotypes. A mathematical model was proposed to integrate phenotypic evolution, microenvironmental acidification, and tumor density dynamics. Three key mechanisms were incorporated in it: frequency-dependent selection favoring acid-resistant cells below a critical pH, stress-induced phenotypic switching, and a positive feedback loop where resistant cells produce excess acid that intensifies selection pressure. The well-posedness of the model was established. Through numerical simulations across biologically relevant parameter regimes, we identified two therapeutically targetable parameters: the baseline acid clearance rate (a proxy for vascular perfusion) and a protection factor (representing acid-resistance "machinery" effectiveness) as critical bifurcation parameters for resistance evolution. The model exhibits qualitatively distinct dynamics depending on phenotypic plasticity levels. In low-plasticity tumors, both parameters exhibit sharp bifurcations with strong parameter interactions: clearance and protection effects are context-dependent, with therapeutic interventions effective only within specific parameter ranges. In high-plasticity tumors, both parameters produce continuous, monotonic responses with independent, additive effects. These regime-dependent dynamics suggest that treatment strategies should adapt to tumor plasticity: in the former, targeting perfusion alone is typically sufficient, though sequential therapy may be required if the perfusion rate approaches or exceeds the bifurcation threshold, whereas in the latter, treatment might benefit from combination therapies addressing both parameters simultaneously. These findings suggest that a low-dimensional model can identify therapeutically targetable parameters governing resistance evolution, suggesting interventions that may prevent or reverse the harmful effect of acid-resistant phenotypes, which are associated with chemotherapy failure, immune evasion, and metastatic progression.