Mathematical Biosciences and Engineering最新文献

Intratumoural epigenetic heterogeneity, which affects the outcome of many cancer treatments, results from stem cell-differentiated cell hierarchy. Cancer stem cells, also known as tumour-initiating cells, are a pluripotent subpopulation of tumour cells capable of creating a tumour clone through self-renewal and differentiation. Oncolytic viral therapy is a category of cancer therapeutics with high specificity in targeting cancer cells while leaving normal cells unharmed. More recently, oncolytic viruses have been developed that target tumour initiating cells with some promising results. The question is what values for virus infectivity and stem cell specificity result in the best clinical outcome. To address this question, we model interactions between uninfected and infected cancer cells, within a stem cell-differentiated cell hierarchy, during oncolytic viral therapy. We calculate the basic reproduction number and use it to constrain the infectivity rates of initiating and differentiated cancer cells. Long-term tumour shrinkage is observable when this constraint is met; otherwise, treatment fails. Our results suggest that stem cell specificity of an oncolytic virus depends both on the average infectivity and mitotic rates of infected cells. There is a positive correlation between the average infectivity rate and stem cell specificity for nonmitotic infected cells: when average infectivity is high, an oncolytic virus with higher stem cell specificity leads to smaller tumours. In contrast, when average infectivity is low, the minimum tumour size is obtained when an oncolytic virus with higher potency targeting differentiated cells is used. For the perfect stem cell targeting regimen, we derive the condition that leads to the minimum tumour size.

This study introduces a novel multivariable optimal control framework for hemodialysis, which uniquely integrates five physiological states (blood urea concentration, fluid volume, blood pressure, electrolytes, and hemoglobin) with three clinically adjustable inputs (ultrafiltration rate, blood flow, and dialysate composition). By employing the limited-memory Broyden-Fletcher-Goldfarb-Shanno-B (L-BFGS-B) algorithm with patient-specific box constraints, the model enforces patient-specific physiological safety limits while dynamically balancing clinical targets. Numerical simulations demonstrate the stabilization of key parameters within ±5% of clinical benchmarks (e.g., KDIGO guidelines), though deviations in the hemodynamic responses underscore the need for adaptive control in real-world scenarios. Urea clearance trajectories align with efficacy patterns observed in practice, while blood pressure fluctuations reveal systematic offsets that require protocol refinement. This work bridges control theory with hemodialysis dynamics, thus offering a simulation-driven foundation for future clinical validation and personalized treatment optimization.

Studying the relationship between Moso bamboo sap flow and environmental factors is essential for understanding the water transpiration patterns of this species. Traditional methods often rely on correlation analysis, but correlation does not imply causation. To elucidate the underlying mechanisms of how major environmental factors influence Moso bamboo sap flow, we analyzed the causality between them. First, the Fast Causal Inference algorithm was used to explore non-temporal causal relationships. Subsequently, the Latent Peter-Clark Momentary Conditional Independence algorithm was employed to further analyze the temporal causal effects. We found causal relationships among factors with low gray correlation coefficients. Besides, illumination, air, and soil temperature promote the density increase of sap flow, while carbon dioxide concentration, air humidity, and soil temperature inhibit bamboo sap flow density overall. Among these factors, illumination exhibits the longest lagged causal effect approximately around 80 minutes, whereas carbon dioxide concentration and soil humidity can quickly affect the sap flow density, with approximately 20 minutes. The study presents a novel methodological approach to analyze the complex interplay between environmental factors and sap flow, providing a more explanatory and logical framework. This study offers a novel methodological framework for disentangling the complex interactions between environmental variables and sap flow, providing deeper insights into the dynamic processes driving Moso bamboo water use. The findings contribute to advancing plant physiology and environmental science, while opening avenues for future research in related fields.

Fishery stock assessments typically rely on biomass estimates derived from stratified random sampling, where a key assumption is a consistent spatial biomass distribution over time. However, climate-driven movements of marine species may be violating this assumption, potentially introducing biases into biomass estimates. To address this, we develop a spatially explicit data-driven mathematical modeling framework where species-specific movement is driven by environmental variables such as water temperature and geographic habitat preferences. To demonstrate this modeling approach we develop spatial simulations for three Atlantic fish species under several temperature scenarios and population trends. We then compute biomass estimates derived from the stratified random samples of the model output, and compare estimates derived from design-based stratified mean to those estimated from a spatio-temporal model-based approach that allows inclusion of environmental covariates. Our modeling framework produces spatial models that include climate-driven changes in biomass distributions, and resulting biomass estimates are impacted by species shifting their spatial densities over time. This framework has broad uses including evaluation of survey designs, management strategy evaluations, climate-driven biomass predictions, and conducting a rigorous statistical assessment for climate-induced bias of specific biomass estimation approaches.

Mathematical modeling and numerical simulation are valuable tools for getting theoretical insights into dynamic processes such as, for example, within-host virus dynamics or disease transmission between individuals. In this work, we propose a new time discretization, a so-called non-standard finite-difference-method, for numerical simulation of the classical target cell limited dynamical within-host HIV-model. In our case, we use a non-local approximation of our right-hand-side function of our dynamical system. This means that this right-hand-side function is approximated by current and previous time steps of our non-equidistant time grid. In contrast to classical explicit time stepping schemes such as Runge-Kutta methods which are often applied in these simulations, the main advantages of our novel time discretization method are preservation of non-negativity, often occurring in biological or physical processes, and convergence towards the correct equilibrium point, independently of the time step size. Additionally, we prove boundedness of our time-discrete solution components which underline biological plausibility of the time-continuous model, and linear convergence towards the time-continuous problem solution. We also construct higher-order non-standard finite-difference-methods from our first-order suggested model by modifying ideas from Richardson's extrapolation. This extrapolation idea improves accuracy of our time-discrete solutions. We finally underline our theoretical findings by numerical experiments.

This paper investigated the stability of nonlinear stochastic systems with distributed-delay impulses within the framework of event-triggered impulsive control (ETIC). A continuous event-triggered mechanism (ETM) with a fixed waiting time and a periodic ETM with a fixed sampling period were proposed, effectively eliminating the occurrence of Zeno behavior. By employing the Lyapunov method and mathematical induction, a set of sufficient conditions was established to ensure the p-th moment uniform stability (p-US) and p-th moment exponential stability (p-ES) of the considered system. Furthermore, the theoretical results were applied to a class of nonlinear stochastic systems. Utilizing the linear matrix inequality (LMI) approach, a joint design of the ETM and impulsive control gains was achieved. Finally, numerical examples were provided to demonstrate the effectiveness and feasibility of the proposed theoretical results.

COVID-19 is a highly transmissible respiratory disease that has significantly impacted global health and economies. In this study, we investigated the impact of immunity duration, vaccination behavior, transmission reduction measures, and healthcare timing and duration on COVID-19 dynamics and economic outcomes. Using a mathematical model that integrates epidemiological, human behavioral, and economic factors, we analyzed the effectiveness of interventions based on real-world data. Analytical results revealed up to six disease-free equilibria, with stability determined by reproduction number thresholds. Results from numerical simulations of the model indicated that prolonged immunity and high vaccination rates can reduce peak infections and deaths, whereas delayed hospitalizations and increased transmission can exacerbate outbreaks. Sensitivity analysis highlights vaccine efficacy and uptake as key determinants of disease control. These findings underscore the need for sustained vaccination, timely healthcare interventions, and strategic public health measures.

In this paper, we present a deterministic model for the population dynamics of HIV/AIDS, wherein some individuals at the severe symptomatic phase of HIV develop serious opportunistic infections (OIs) such cryptococcal, tuberculous, pneumococcal, and other bacterial meningitis due to an inappropriate treatment or lack of counseling. OIs are responsible for significant mortality and disability on individuals with HIV in many countries. Cryptococcal meningitis (CM) is among frequent OIs responsible for significant mortality and disability of individuals with HIV in limited resource settings. However, there are also cases of high mortality due to CM on HIV-uninfected individuals, but the burden of CM is more frequent in people living with HIV. We proved the global stability of the disease-free as well as the endemic equilibrium points. In addition, we performed the study of sensitivity analysis of the basic reproduction number with the parameters of the model as well as with some compartmental classes. We illustrated our theoretical results by way of numerical simulations using a projection on the HIV historical data of South Africa since 2024. Our analysis showed that a combination of ART and OI specific treatments may reduce the number of death related cases.

Short-term wind speed forecasting is essential for enhancing the efficiency and dependability of wind renewable energy installations. Although often used, conventional point predictions generated by machine learning techniques frequently fail to accurately capture the natural uncertainty associated with wind speed variation. Modeling this type of uncertainty is crucial for providing credible information as the level of uncertainty increases. Prediction intervals (PIs) offer a probabilistic framework for quantifying forecast uncertainty. This paper presents a hybrid forecasting methodology that combines support vector regression (SVR) with adaptive kernel density estimation (AKDE) to estimate wind speed prediction intervals over various short-term horizons (10, 30, 60, and 120 minutes). In contrast to standard kernel density estimation (KDE), which employs a uniform bandwidth and may overlook local data attributes, the adaptive KDE approach adjusts the bandwidth in accordance with the local distribution of forecast errors, thereby facilitating more precise and locally tuned uncertainty quantification. The efficacy of the proposed SVR-AKDE model is evaluated against conventional KDE-based interval estimation. Outcomes are assessed by recognized PI quality indicators, including prediction interval coverage probability (PICP), prediction interval normalized average width (PINAW), and coverage width-based criterion (CWC). Simulation findings confirm the efficacy of our approach and demonstrate that the SVR-AKDE-based PI forecasting consistently provides enhanced coverage and narrower widths compared to traditional KDE. This approach provides a comprehensive solution for short-term wind speed forecasting with quantifiable uncertainty, therefore enhancing its application in operational wind energy control.

This paper was mainly concerned with the asymptotic dynamics of stochastic diffusive coral reef ecosystems with Lévy noise. First, we proved the well-posedness and energy estimates of solution. Second, under some suitable conditions, we proved the existence and uniqueness of weak pullback mean random attractors and invariant measures. Finally, a large deviation principle result for solutions of stochastic diffusive coral reef ecosystems with Lévy noise was obtained by a variational formula for positive functionals of a Poisson random measure and the method of weak convergence. Interestingly, this showed the effect of Lévy noise which can stabilize or destabilize systems, which was significantly different from the classical Brownian motion process.