Mathematical Biosciences and Engineering最新文献

In this paper, we present a novel design of an observer-based event-triggered impulsive control strategy for delayed reaction-diffusion neural networks subject to impulsive perturbation. The impulsive instants of impulsive control are determined in an event-triggered way, and the control strength is designed by the sampling output of an impulsive observer. Several criteria with Lyapunov conditions and linear matrix inequalities are established for the global exponential stability of delayed reaction-diffusion neural networks. It inherits the advantages of event-triggered impulsive control such as low triggering frequency and high efficiency, and is applicable for networks with unmeasurable states. Finally, the effectiveness of theoretical results is verified by a numerical example.

This work investigates the minimum eradication time in a controlled susceptible-infectious-recovered model with constant infection and recovery rates. The eradication time is defined as the earliest time the infectious population falls below a prescribed threshold and remains below it. Leveraging the fact that this problem reduces to solving a Hamilton-Jacobi-Bellman (HJB) equation, we propose a mesh-free framework based on a physics-informed neural network to approximate the solution. Moreover, leveraging the well-known structure of the optimal control of the problem, we efficiently obtain the optimal vaccination control from the minimum eradication time using the dynamic programming principle. To improve training stability and accuracy, we incorporate a variable scaling method and provide theoretical justification through a neural tangent kernel analysis. Numerical experiments show that this technique significantly enhances convergence, reducing the mean squared residual error by approximately 80% compared with standard physics-informed approaches. Furthermore, the method accurately identifies the optimal switching time. These results demonstrate the effectiveness of the proposed deep learning framework as a computational tool for solving optimal control problems in epidemic modeling as well as the corresponding HJB equations.

Ever since Tsallis introduced Tsallis entropy theory, it has been applied to a wide variety of topics in physics and chemistry, with new applications being discovered annually. The amount of research suggests that the Tsallis entropy concept holds significant potential. This paper introduces weighted cumulative residual Tsallis entropy (WCRTE) and weighted cumulative past Tsallis entropy (WCPTE), as well as their dynamic counterparts for the concomitants of $ m $-generalized order statistics ($ m $-GOSs) derived from the Farlie-Gumbel-Morgenstern bivariate family. The characteristics of the proposed entropy measures were analyzed, demonstrating their ability to characterize the Pareto and exponential distributions. Applications of these findings were presented for order statistics (OSs) systems and record values with uniform, Weibull, and power marginal distributions. Furthermore, the empirical alternatives WCRTE and WCPTE were proposed for calculating new information measures. Two real-world data sets have been evaluated for illustrative purposes, demonstrating satisfactory performance.

Chronic myelogenous leukemia (CML) is a cancer of the white blood cells that results from uncontrolled growth of myeloid cells in the bone marrow and the accumulation of these cells in the blood. The most common form of treatment for CML is imatinib, a tyrosine kinase inhibitor. Although imatinib is an effective treatment for CML and most patients treated with imatinib do attain some form of remission, imatinib does not completely eradicate all leukemia cells, and if treatment is stopped, all patients eventually relapse. Kim et al. constructed a system of delay differential equations to mathematically model the dynamics of anti-leukemia T-cell responses to CML during imatinib treatment, and demonstrated the usefulness of the mathematical model for studying novel treatment regimes to enhance imatinib therapy. Paquin et al. demonstrated numerically using this DDE model that strategic treatment interruptions (STIs) may have the potential to completely eradicate CML in certain cases. We conducted a comprehensive numerical study of the model parameters to identify the mathematical and numerical significance of the individual parameter values on the efficacy of imatinib treatment of CML. In particular, we analyzed the effects of the numerical values of the model parameters on the behavior of the system, revealing critical threshold values that impact the ability of imatinib treatment to achieve remission and/or elimination. We also showed that STIs provide improvements to these critical values, categorizing this change as it relates to parameters inherent to either CML growth or immune response.

Microbial communities are constantly challenged by environmental stochasticity, rendering time-series data obtained from these communities inherently noisy. Traditional mathematical models, such as the first-order multivariate autoregressive (MAR) model and the deterministic generalized Lotka-Volterra model, are no longer suitable for predicting the stability of a microbiome from its time-series data, as they fail to capture volatility in the environment. To accurately measure microbiome stability, it is imperative to incorporate stochasticity into the existing mathematical models in microbiome research. In this paper, we introduce a stochastic generalized Lotka-Volterra (SgLV) system that characterizes the temporal dynamics of a microbial community. To study this system, we developed a comprehensive theoretical framework for calculating four resilience measures based on the SgLV model. These resilience metrics effectively capture the short- and long-term behaviors of the resilience of the microbiome. To illustrate the practical application of our approach, we demonstrate the procedure for calculating the four resilience measures using simulated microbial abundance datasets. The procedural simplicity enhances its utility as a valuable tool for application in various microbial and ecological communities.

The fitness of an annual plant can be thought of as how much fruit is produced by the end of its growing season. Working under the assumption that annual plants grow to maximize fitness, we use optimal control theory to understand this process. We introduce a model for resource allocation in annual plants that extends classical work by Iwasa and Roughgarden to a case where both carbohydrates and mineral nutrients are allocated to shoots, roots, and fruits. We use optimal control theory to determine the optimal resource allocation strategy for the plant throughout its growing season as well as develop a numerical scheme to implement the model. We find that fitness is maximized when the plant undergoes a period of mixed vegetative and reproductive growth prior to switching to reproductive-only growth at the end of the growing season. Our results further suggest that what is optimal for an individual plant is highly dependent on initial conditions, and optimal growth has the effect of driving a wide range of initial conditions toward common configurations of biomass by the end of a growing season.

Tick-borne illnesses are transmitted to mammals like rodents and deer by infected ticks. These illnesses have shown dramatic increase in recent times, thereby increasing public health risk in the United States. Additionally, these mammals can be impacted by predation and the fear of their predators. In this study, we modeled the lethal and non-lethal effect of predation of the mammals on the dynamics of tick-borne disease using ehrlichiosis as our model disease system. Results of the theoretical analysis of reduced form of the model indicate that the model equilibria are stable when the tick fecundity and mortality rates are not host dependent. Furthermore, predator-induced fear and predator attack rates are two of the significant parameters of the model outputs from the sensitivity analysis carried out. Numerical simulation of the model shows that the combined impact of both lethal and non-lethal predation sets off a cascading chain reaction leading to a corresponding reduction in the prey and tick populations; in particular there are more infected larvae when infected prey population are low and few infected larvae when there are more infected prey. Similar dynamics was observed for the infected nymphs and adult ticks and infected predator population. Furthermore as the fear of the predator increases, the prey population reduces which subsequently lead to a decrease in the tick populations and subsequently disease in the community.

We constructed a compartmental mathematical model to study the dynamics of viral sexually transmitted infections (STIs) in a population consisting of men and women who engage in sexual contact with both sexes. Each sex is further split into compartments of susceptible, infected/infectious, and recovered/immune individuals, with constant per capita recovery and loss of immunity rates, while the per capita infection rates for each sex (force of infection) are based on standard incidence terms corresponding to the probabilities that the sexual partner of each sex that a susceptible individual randomly selects is an infected one. We explored possible effects of behavioral interventions, such as condom usage and reducing the number of sexual partnerships as well as the different dynamics of STI transmission between populations engaging solely in opposite-sex interactions and those engaging in non-opposite-sex interactions. These findings can help inform the development of public health policies aimed at alleviating the burden of sexually transmitted diseases.

This paper investigated the synchronization issue of uncertain chaotic neural networks (CNNs) using a delayed impulsive control approach. To address the disturbances caused by parameter uncertainty and the flexibility of impulsive delays, the concept of average impulsive delay (AID) and average impulsive interval (AII) were utilized to handle the delays as a whole. Under the condition that the norms of uncertain parameters are bounded, the synchronization criteria for uncertain CNNs were derived based on linear matrix inequalities (LMIs). Specifically, we relaxed the constraints on the delay in the impulsive control inputs, thus allowing it to flexibly vary without being bound by some conditions, which provides a broader applicability compared to most existing results. Additionally, the results show that delayed impulses can facilitate the synchronization of uncertain CNNs. Finally, the validity of the theoretical results was verified through a numerical example.

The central question in this paper is the character and role of the within-host and between-host interactions in vector-transmitted diseases compared to environmental-transmitted diseases. In vector-transmitted diseases, the environmental stage becomes the vector population. We link an epidemiological model for a vector-transmitted disease with a simple immunological process: the effective transmission rate from host to vector, modeled as a function of the infected cell level within the host, and a virus inoculation term that depends on the abundance of infected mosquitoes. We explore the role of infectivity (defined as the number of host target cells infected), recovery rate, and viral clearance rate in the coupled dynamics of these systems. As expected, the conditions for a disease outbreak require the average individual in the population to have an active (within-host) viral infection. However, the outbreak's nature, duration, and dynamic characteristics depend on the intensity of the within-host infection and the nature of the mosquito transmission capacity. Through the model, we establish inter-relations between the infectivity, host recovery rate, viral clearance rate, and different dynamic behavior patterns at the population level.