Mathematical medicine and biology : a journal of the IMA最新文献

Biofilm infections on medical implants are difficult to eradicate because insufficient nutrient availability promotes antibiotic-tolerant persister cells that survive treatment and reseed growth. Existing mathematical models usually omit nutrient-dependent phenotypic switching between proliferative and persister states. Without this mechanism, models cannot capture how environmental conditions control the balance between active growth and dormancy, which is central to biofilm persistence. We present a continuum model that couples nutrient transport with the dynamics of proliferative bacteria, persisters, dead cells, and extracellular polymeric substances. The switching rates between proliferative and persister phenotypes depend on local nutrient concentration through two thresholds, enabling adaptation across nutrient-poor, intermediate, and nutrient-rich regimes. Simulations show that nutrient limitation produces a high and sustained proportion of persister cells even when biomass is reduced, whereas nutrient-rich conditions support reversion to proliferative growth and lead to greater biomass. The model also predicts that persister populations peak at times that vary with nutrient availability, and these peaks coincide with turning points in biofilm growth, identifying critical intervention windows. By directly linking nutrient availability to phenotypic switching, our model reveals mechanisms of biofilm persistence that earlier models could not capture, and it points toward strategies that target nutrient-driven adaptation as a means to improve the control of implant-associated infections.

From 1999 to 2022, nearly 300,000 people died from overdoses involving prescription opioids. Commonly used for the management of acute post-surgical pain, prescription opioids remain a leading cause of opioid misuse and abuse. Among surgical populations, patients who undergo hand surgery have especially high rates of prolonged post-operative opioid use and opioid use disorder (OUD). We built a compartmental model describing the progression from opioid exposure to OUD in hand surgery patients and parameterized it using empirical patient data. Using this model, we investigated the functional relationship between the number of opioid prescriptions received and opioid abuse. We found that, depending on the response curve used to describe opioid addiction risk, different numbers of prescriptions pose higher risks than others, advancing our understanding of how prescription patterns influence OUD development.

In Single Photon Emission Computed Tomography (SPECT), the image reconstruction process involves many tunable parameters that have a significant impact on the quality of the resulting clinical images. Traditional image quality evaluation often relies on expert judgment and full-reference metrics such as Mean Squared Error (MSE) and Structural Similarity Index (SSIM). However, these approaches are limited by their subjectivity or the need for a ground-truth image. In this paper, we investigate the usage of a No-Reference Image Quality Assessment (NR IQA) method in SPECT imaging, employing the Perception-based Image QUality Evaluator (PIQUE) score. Precisely, we propose a novel application of PIQUE in evaluating SPECT images reconstructed via filtered backprojection using a parameter-dependent Butterworth filter. For the optimization of filter's parameters, we adopt a kernel-based Bayesian optimization framework grounded in reproducing kernel Hilbert space theory, highlighting the connections to recent greedy approximation techniques such as P- and f -greedy. Experimental results in a concrete clinical setting for SPECT imaging show the potential of this optimization approach for an objective and quantitative assessment of image quality, without requiring a reference image.

The study of the dynamics of an infectious disease is fundamental to understanding its community spread. These include obtaining estimates for transmission rates, recovery rates and the average number of secondary cases per infectious case (reproduction number). Social behaviors, control measures, environmental conditions and long recovery times result in time varying parameters. Further, imperfect data and many uncertainties lead to inaccurate estimations. This is particularly true in third-world countries, where a greater proportion of people with mild infections may not seek medical treatment. Data on the prevalence of COVID-19 provides an excellent source for case studies to analyse time-dependent parameters. Using Sri Lankan COVID-19 data, we demonstrate how one could utilize Itô stochastic differential equations with a gamma distribution correction to estimate disease transmission parameters as a function of time. As we illustrated here, the model is well-suited for forecasting the dates of peak prevalence and the number of new cases using the estimated parameters.

This study presents a mathematical model describing cloned hematopoiesis in chronic myeloid leukemia $text{(CML)}$ through a nonlinear system of differential equations. The primary objective is to understand the progression from healthy hematopoiesis to the chronic and accelerated-acute phases in myeloid leukemia. The model incorporates intrinsic cellular division events in hematopoiesis and delineates the evolution of chronic myeloid leukemia into five compartments: cycling stem cells, quiescent stem cells, progenitor cells, differentiated cells and terminally differentiated cells. Our analysis reveals the existence of three distinct non-zero steady states within the dynamical system, representing healthy hematopoiesis, the chronic phase and the accelerated-acute stage of the disease. We investigate the local and global stability of these steady states and provide a characterization of the hematopoietic states based on this analysis. Additionally, numerical simulations are included to illustrate the theoretical results.

Delineating the dynamics of highly lethal anthrax disease in a biosecured livestock farm and impact of anthrax vaccination is presented through a modified deterministic $SIRBV$ model incorporating nonlinear ratio-dependent disease transmission rate. The basic reproduction number $(R_{0})$ of the system is computed and employed to explore the existence and asymptotic stability around the steady states of the system. The system experiences transcritical bifurcation at the disease-free steady state for $R_{0} = 1$. Waning of recovery-derived immunity and vaccination-derived immunity trigger backward bifurcation causing reemergence of anthrax in livestock. The dynamical behaviors of the fractional order system express that increased immunological memory will benefit to cut down the eradication time of anthrax transmission from the system. Numerical simulations suggest that appropriate vaccination and comprehensive biosecurity protocols would help to prevent the anthrax transmission and control the disease-induced deaths of cattle.

An infectious disease such as COVID-19 posed a threat to public health worldwide due to its high infection rate and its further mutation into novel variants. Vaccination serves as a vital tool to interrupt its transmission cycle and far-reaching effects. However, the effectiveness of vaccination depends upon a well-planned strategy. This study explores the comparison between full and partial vaccination strategies using a novel fractional SVIR mathematical model with Caputo fractional derivative. The model categorizes vaccinated individuals into two groups: partially and fully vaccinated class. To account for limited medical resources and virus reemergence, we adopt the Holling type III saturated treatment function for treatment rate. In the analysis, we first show well posedness of model solutions. Further, we discuss the stability of the two equilibria exhibited by the system: DFE (Disease Free Equilibrium) and EE (Endemic Equilibrium). It is shown that the DFE is locally asymptotically stable when R0 < 1, and EE is locally asymptotic stable by Routh-Hurwitz criterion. Moreover, both the equilibrium points are proved to be globally asymptotically stable under certain conditions with the help of appropriate Lyapunov function. Numerical simulations are also performed to validate the analytical findings using MATLAB. The quantification of effects of partial and full vaccination reveals that full vaccination results in higher percentage of recovered population, making it evident that policymakers and professionals should focus on the implications of effective full vaccination among susceptible individuals.

One of the hallmarks of Alzheimer's disease (AD) is the accumulation and spread of toxic aggregates of tau protein. The progression of AD tau pathology is thought to be highly stereotyped, which is in part due to the fact that tau can spread between regions via the white matter tracts that connect them. Mathematically, this phenomenon has been described using models of 'network diffusion,' where the rate of spread of tau between brain regions is proportional to its concentration gradient and the amount of white matter between them. Although these models can robustly predict the progression of pathology in a wide variety of neurodegenerative diseases, including AD, an underexplored aspect of tau spreading is that it is governed not only by diffusion but also by active transport along axonal microtubules. Spread can therefore take on a directional bias, resulting in distinct patterns of deposition, but current models struggle to capture this phenomenon. Recently, we have developed a mathematical model of the axonal transport of toxic tau proteins that takes into account the effects tau exerts on the molecular motors. Here we describe and implement a macroscopic version of this model, which we call the Network Transport Model (NTM). A key feature of this model is that, while it predicts tau dynamics at a regional level, it is parameterized in terms of only microscopic processes such as aggregation and transport rates, i.e., differences in brain-wide tau progression can be explained by its microscopic properties. We provide numerical evidence that, as with the two-neuron model that the NTM extends, there are distinct and rich dynamics with respect to the overall rate of spread and the staging of pathology when we simulated the NTM on the hippocampal subnetwork. The theoretical insights provided by the NTM have broad implications for understanding AD pathophysiology more generally.

The linear functional analysis, historically founded by Fourier and Legendre (Fourier's supervisor), has provided an original vision of the mathematical transformations between functional vector spaces. Fourier, and later Laplace and Wavelet transforms, respectively, defined using the simple and damped pendulum have been successfully applied in numerous applications in Physics and engineering problems. However, the classical pendulum basis may not be the most appropriate in several problems, such as biological ones, where the modelling approach is not linked to the pendulum. Efficient functional transforms can be proposed by analyzing the links between the physical or biological problem and the orthogonal (or not) basis used to express a linear combination of elementary functions approximating the observed signals. In this study, an extension of the Fourier point of view called Dynalet transform is described. The approach provides robust approximated results in the case of relaxation signals of periodic biphasic organs in human physiology.