Mathematical Biosciences and Engineering最新文献

In this study, we present a unified mathematical model for tuberculosis (TB) that integrates key interventions: Mask use and media campaigns to raise community awareness and promote vaccine booster uptake. The model also incorporates slow-fast disease progression and limited treatment capacity. A mathematical analysis was conducted to determine the existence and stability of equilibrium points. From the mathematical analysis on the stability criteria of the TB-free equilibrium point, we show that TB can be eradicated if the basic reproduction number is below one. However, due to insufficient treatment capacity, a backward bifurcation may occur when the reproduction number equals one, enabling the coexistence of endemic and disease-free equilibria even when the reproduction number is below one. The parameter estimation is based on TB incidence data per 100,000 individuals in Indonesia. Sensitivity analysis reveald that although both interventions are effective, media campaigns combined with vaccine boosters are more impactful in reducing TB transmission than the use of masks. Numerical simulations further suggest the possibility of periodic outbreaks, indicating potential seasonal TB patterns. To explore adaptive intervention strategies, we extended the model using an optimal control framework. Our findings suggested that combined implementation of face masks and media campaigns is more effective than using either alone, particularly when the likelihood of rapid disease progression increases.

In this article, we considered a Bayesian approach to estimating the evolution of the COVID-19 pandemic in Ecuador, providing the first rigorous analysis of its progression in the country. Specifically, we applied variational data assimilation to estimate the parameters and initial conditions of a compartmental SARS-CoV-2 propagation model while accounting for structural data uncertainty through error covariance matrices. These optimized parameters correspond to maximum-a-posteriori (MAP) estimates, which, in a second stage, allow us to infer the posterior distribution of the parameters. We considered two different data sources: the official count of positive COVID-19 tests from the Ecuadorian Public Health Ministry (MSP) and an estimate of COVID-19-related deaths derived from excess mortality data recorded by the Ecuadorian Civil Registry (RC). We regard RC data as the closest approximation to the actual number of COVID-19 cases. The results highlight that, although there are differences between the estimates obtained using MSP data-generated in real time during the pandemic-and those based on positive cases inferred from excess mortality, the trends in the computed effective reproduction numbers coincide. This suggests that the methodology presented in this paper, and applied in real time during the pandemic, was able to accurately capture the evolution of the pandemic in Ecuador. Additionally, we conducted a comparative analysis of Ecuador's two most populous provinces, Pichincha and Guayas, which experienced the pandemic very differently, particularly in its initial stages. This study aimed to improve our understanding of the virus's spread in these provinces and provide insights into how epidemiological dynamics can vary within the same country.

This paper deals with the multiscale derivation of a nonlinear stochastic chemotaxis-haptotaxis system of cancerous tissue invasion from a new stochastic kinetic theory model based on the micro-macro decomposition technique. We show that this approach technically can lead to some systems known in the literature, such as the filling volume effect, and a new system by taking the stochasticity effect and nonlocal diffusion into account. We develop an asymptotic-preserving numerical scheme to solve the obtained equivalent micro-macro formulation numerically. The objective is to provide a uniformly stable scheme regarding the small parameters and consistency with the diffusion limit. Various numerical examples validate the proposed approach. Finally, we provide numerical simulations in the two-dimensional setting obtained by the macroscopic stochastic model.

Several pests and diseases are major factors challenging the coffee industry worldwide. Particularly, production of Coffee Arabica in many African countries has been affected by Hypothenemus hampei and Colletotrichum kahawae in a coffee farm. Pest(s) and disease(s) are commonly inter-related and can interact, because pests and pathogens have the same biophysical requirements in ecosystems. Assessment of coffee berries damage due to multiple pests and diseases is a necessary step in designing appropriate control strategies. In this paper, we developed a mathematical model describing the co-dynamics of Hypothenemus hampei (coffee berry borer, CBB) and Colletotrichum kahawae (coffee berry disease, CBD). The model used a system of nonlinear ordinary differential equations to capture the interactions among the CBB pest population, the CBD fungal pathogen, and the healthy and infected coffee berry populations. Optimal control strategies were also incorporated to assess effective management approaches. Optimal control strategies were obtained by minimizing the number of pests and fungal pathogen population by incorporating two control variables such as biological control and cultural practices. The existence of optimal controls was examined using Pontryagin's minimum principle. The Hamiltonian was constructed, and adjoint equations were solved to minimize the cost functional. Lastly, from different scenarios, the numerical simulations were performed to illustrate the model's co-dynamics with and without optimal control strategies.

Multi-scale dispersion entropy (MDE) has been extensively applied to capture the nonlinear features of electroencephalography (EEG) signals for fatigue driving detection. However, MDE suffers from information loss and limited robustness during the extraction of EEG signal nonlinearities. To address these issues, a fatigue driving detection approach integrating local maximum refined composite multi-scale normalized dispersion entropy (LMRCMNDE) with support vector machines (SVM) is introduced. To begin, the refined composite multi-scale dispersion entropy (RCMDE) technique is presented. Next, the segmented averaging in the coarse-graining process is substituted with local maximum calculation to alleviate information loss. Finally, normalization of the entropy values is performed to enhance the robustness of feature parameters, leading to the formation of LMRCMNDE. LMRCMNDE serves as the feature descriptor for fatigue driving EEG signals, while SVM is employed for classification. Compared with the MDE-SVM and RCMDE-SVM approaches, the LMRCMNDE-SVM method achieves higher recognition accuracy, reaching up to 98%. The proposed method can effectively identify the fatigue state of drivers and provide a new reliable detection method for automatic fatigue driving detection.

The movement of intracellular cargo transported by molecular motors is commonly marked by switches between directed motion and stationary pauses. The predominant measure for assessing movement is effective diffusivity, which predicts the mean-squared displacement of particles over long timescales. In this work, we considered an alternative analysis regime that focused on shorter timescales and relied on automated segmentation of paths. Due to intrinsic uncertainty in changepoint analysis, we highlighted the importance of statistical summaries that were robust with respect to the performance of segmentation algorithms. In contrast to effective diffusivity, which averaged over multiple behaviors, we emphasized tools that highlighted the different motor-cargo states, with an eye toward identifying biophysical mechanisms that determined emergent whole-cell transport properties. By developing a Markov chain model for noisy, continuous, piecewise-linear microparticle movement, and associated mathematical analysis, we provided insight into a common question posed by experimentalists: how does the choice of observational frame rate affect what is inferred about transport properties?

In this article, we focused on the study of codimension-one Hopf bifurcations and the associated Lyapunov stability coefficients in the context of general two-dimensional reaction-diffusion systems defined on a finite fixed-length segment. Algebraic expressions for the first Lyapunov coefficients are provided for the infinite-dimensional system subject to Neumann boundary conditions. As an application, a diffusive predator-prey system modeling competing populations with a Holling type-II functional response for the predator was analyzed and studied under Neumann boundary conditions. Our main goal is to perform a detailed, local stability analysis of the proposed model, showing the existence of multiple spatially homogeneous and non-homogeneous periodic orbits, arising from the occurrence of a codimension-one Hopf bifurcation.

In this paper, we use a variety of mathematical models to characterize the early phase of the COVID-19 pandemic in New Mexico. We use both empirical and mechanistic models based on differential equations to examine the dynamics of the pandemic in New Mexico and in carefully selected New Mexico counties. For the empirical model, we use the exponential growth model to compute and estimate the growth rate, basic reproduction number $ mathcal{R}_0 $ and effective reproduction number $ mathcal{R}_t $. In addition, we use the SIR model to estimate $ mathcal{R}_0 $, using the new weekly COVID cases and also cumulative cases. We found that for the beginning of the early phase of the pandemic, the most populous counties had basic reproduction numbers greater than one. In addition, it was found that the transmission rates of some counties varied significantly during the early phase of the pandemic. Moreover, $ mathcal{R}_0 $ dropped below one during some phases for some counties when using the SIR model. This suggests that non-pharmaceutical interventions had some impact on reducing the burden of the pandemic and that people's behavior changed during this early phase.

Tuberculosis stands as the leading cause of death worldwide, driven by infection from a single bacterial agent, and has been recognized as a global public health concern by the World Health Organization. Recent studies highlight that the innate immune response has a central role in controlling the initial spread of Mycobacterium tuberculosis (Mtb) within the host, and triggers adaptive immune response. We developed and analyzed a model examining the interactions among macrophages, innate cells, and Mtb to determine whether the infection is controlled by the innate immune response or whether a specific adaptive response is triggered. Findings suggest that if an individual infected by Mtb has an adequate immunological state to prevent bacteria from infecting the macrophage population (that is, if the external bacteria engulfed by macrophages are eliminated by them, or if their capacity to replicate inside them is limited), then the innate immune response will effectively control the primary infection.

Understanding the metabolic adaptations of cancer cells is crucial for uncovering potential therapeutic targets and improving treatment strategies. In this study, we present a hybrid modeling framework that combines Physics-Informed Neural Networks (PINNs) and Universal PINNs (UPINNs) to investigate glucose-lactate metabolism in glioblastoma cell lines. We first employed PINNs to infer critical model parameters governing glucose uptake and phenotypic switching in tumor cells, demonstrating high accuracy using synthetic data. We then extended this framework using UPINNs to uncover hidden metabolic dynamics that could not be explicitly modeled, introducing a latent variable $ W $ to represent unknown functional behavior in glycolytic processes. Our approach was validated for both synthetic and experimental datasets for two glioblastoma cell lines (LN18 and LN229) with distinct metabolic phenotypes. The UPINN framework not only captured cell-type-specific behaviors but also remained robust in the presence of moderate experimental noise. Furthermore, we explored the sensitivity of the model to the trade-off between data fidelity and mechanistic constraints, showing that the choice of loss term weighting significantly impacts predictive performance. While our application centered on cancer metabolism, the proposed method was general and applicable to a wide range of systems described by differential equations, including problems in biology, engineering, and physical sciences. This work demonstrates the potential of UPINNs as a powerful and interpretable tool for data-driven discovery in partially observed dynamical systems.