Bulletin of Mathematical Biology最新文献

HIV-1 remains a formidable global health challenge, as complete viral eradication is still unattainable despite considerable advances in combination antiretroviral therapy (cART). To address this, we develop a stochastic differential equation (SDE) model that incorporates environmental noise into a classical HIV-1 infection dynamics framework, establishing two key advances. Mathematically, we derive the stochastic basic reproduction number $R^s$ and establish the corresponding threshold dynamics: when $R^s<1$ (under mild conditions), the infection is almost surely cleared, whereas for $R^s>1$ , the virus persists stochastically, following an ergodic stationary distribution. Epidemiologically, we demonstrate that environmental noise profoundly influences HIV-1 dynamics and reaffirm the central role of cART. Using optimal control theory, we evaluate three intervention strategies: Strategy 1 (cART enhancement), Strategy 2 (immune modulation), and Strategy 3 (a combined cART-immune approach). Both statistical indicators and dynamical outcomes confirm that Strategy 3 provides a clear advantage in promoting rapid viral suppression by integrating cART enhancement with immune modulation. Moreover, we observe that this combined intervention remains highly effective even under stringent cost constraints, and further reductions in intervention cost could improve its cost-efficiency. These results provide not only a novel theoretical framework for understanding HIV-1 infection dynamics, but also actionable clinical insights for optimizing treatment protocols, underscoring the critical importance of cost considerations in HIV-1 management.

Digital twins (DTs) have emerged in recent years as a very promising technology for individualized health management and recovery. Each DT is built upon a computational model that captures some aspect of human biology and is typically intended to be used with individuals to either restore their health or maintain it. In many cases, DT projects reach "from bench to bedside" and often involve commercialization to bring the final product to the end-user. The purpose of this perspective is to highlight DT technology as an opportunity for the mathematical modeling community and look at DT development from both the academic and commercial viewpoints. Since DT technology is applied widely in biology, beyond health care, there are several references at the end to applications in ecology, biotechnology, agriculture, and synthetic biology.

We study a stochastic model of a copolymerization process that has been extensively investigated in the physics literature. The main questions of interest include: (i) what are the criteria for transience, null recurrence, and positive recurrence in terms of the system parameters; (ii) in the transient regime, what are the limiting fractions of the different monomer types; and (iii) in the transient regime, what is the speed of growth of the polymer? Previous studies in the physics literature have addressed these questions using heuristic methods. Here, we utilize rigorous mathematical arguments to derive the results from the physics literature. Moreover, the techniques developed allow us to generalize to the copolymerization process with finitely many monomer types. We expect that the mathematical methods used and developed in this work will also enable the study of even more complex models in the future.

Gene expression is inherently stochastic, and transcription initiation is a key source of variability across cells. While classical promoter models often assume linear state transitions, emerging evidence suggests more flexible promoter architectures. Here we introduce a generalized cyclic promoter model and compare it with the standard linear model using exact analytical solutions for initiation-time and nascent RNA distributions. Our results reveal that linear promoters produce only monotonic initiation-time statistics and a limited set of RNA expression patterns, whereas cyclic promoters generate non-monotonic initiation-time distributions and richer RNA profiles, including multimodal cases not achievable with linear architectures. We further show that cyclic promoters consistently buffer variability in initiation timing and RNA output, providing tighter control over transcriptional noise. Within the cyclic model, the number of exit pathways serves as a tunable parameter that shifts distributions from bimodal to unimodal and reduces noise, offering a potential mechanism for balancing robustness with flexibility in gene regulation. This framework highlights promoter topology as a critical determinant of transcriptional heterogeneity, bridges initiation dynamics with RNA-level variability, and generates testable predictions that can guide single-cell experiments probing promoter structure.

Understanding the interactions between cells and the extracellular matrix (ECM) during collective cell invasion is crucial for advancements in tissue engineering, cancer therapies, and regenerative medicine. This study focuses on the roles of contact guidance and ECM remodelling in directing cell behaviour, with a particular emphasis on exploring how differences in cell phenotype impact collective cell invasion. We present a computationally tractable two-dimensional hybrid model of collective cell migration within the ECM, where cells are modelled as individual entities and collagen fibres as a continuous tensorial field. Our model incorporates random motility, contact guidance, cell-cell adhesion, volume filling, and the dynamic remodelling of collagen fibres through cellular secretion and degradation. Through a comprehensive parameter sweep, we provide valuable insights into how differences in the cell phenotype, in terms of the ability of the cell to migrate, secrete, degrade, and respond to contact guidance cues from the ECM, impacts the characteristics of collective cell invasion.

Hepatitis B virus (HBV) is considered as an etiological agent of the lethal liver disease hepatitis B. In spite of being non-infectious in nature, sub-viral particles (SVPs), composed of mainly viral surface proteins, play critical roles in the persistence and progression of the infection. In this work, it is aimed to study the impacts of SVPs including the effects of capsid recycling. The effects of spatial mobility of capsids, viruses, SVPs and antibodies are also considered. This study illustrates how the dynamics of the infection are affected by multi-point initial conditions. The proposed model consists of a system of partial differential equations. This system is of parabolic type in nature. In order to numerically solve it, the well-known Forward Time Centered Space scheme is applied. The values of the parameters are taken from existing literature. The simulation results show that SVPs can significantly enhance intracellular viral replication and gene expression by reducing the neutralization of virus particles by antibodies. The recycling of capsids also substantially increases the concentration of SVPs. The experiments which are carried out on single-point as well as multi-point initial conditions show that as the number of initial infection points increases, the peaks of infected hepatocytes, viruses and SVPs become higher and occur earlier. The outcomes of the proposed model strongly recommend to consider the diffusion term while HBV infection dynamics are studied. In addition, if the liver is infected at more than one point, infection propagates rapidly; however, the severity of the infection remains same regardless of the number of initial infection points. Based on the findings, some future therapeutic approaches are informed.

Asthma pathogenesis involves activities of other T helper (Th) cells, such as Th17 cells, apart from the known Th1-Th2 cell interaction due to its severity. Pro-inflammatory cytokines, Interleukin (IL)-23/IL-1 $\beta$ mainly produced by macrophages, are considered essential for differentiating Th17 cells, which mediate neutrophilic inflammation (a major inflammatory characteristic of severe asthma, and resistant to available therapy). Variations in allergen exposure can induce distinct inflammatory phenotypes: an eosinophilic phenotype mediated by Th2 cells, a neutrophilic phenotype mediated by Th17 cells, or a mixed phenotype in severe asthma. We developed a mathematical model describing the regulation of Th2 cells, Th17 cells, and macrophages, incorporating IL-23/IL-1 $\beta$ cytokines under varying allergen exposure levels to predict potential therapeutic intervention conditions. The model exhibited two steady-state scenarios corresponding to the absence and presence of allergen, characterized by a transcritical forward bifurcation and mono-, bi-stability with hysteresis reflecting asthma severity, respectively. Bifurcation analysis predicted that the secretion rate of IL-23/IL-1 $\beta$ cytokines, together with the leaving rate of macrophages, are significant factors influencing neutrophilic inflammation. These findings suggest that modulating these parameters may offer effective therapeutic strategies to control asthma severity and shift the system further towards a healthier outcome.

This paper illustrates a further application of topological data analysis to the study of self-organising models for chemical and biological systems. In particular, we investigate whether topological summaries can capture the parameter dependence of pattern topology in reaction diffusion systems, by examining the homology of sublevel sets of solutions to Turing reaction diffusion systems for a range of parameters. We demonstrate that a topological clustering algorithm can reveal how pattern topology depends on parameters, using the chlorite-iodide-malonic acid system, and the prototypical Schnakenberg system for illustration. In addition, we discuss the prospective application of such clustering, for instance in refining priors for detailed parameter estimation for self-organising systems.

We present a mathematical model describing the interactions between cancer cells, cytotoxic T lymphocytes (CTLs), and monocytes within the tumor microenvironment. The model incorporates key immunological mechanisms, including tumor antigenicity, the Allee effect, and monocyte-mediated immune activation via MHCI cross-dressing. Using systems of nonlinear ordinary differential equations (ODEs), we derive analytical expressions for equilibrium points, evaluate their stability, and characterize bifurcations, such as saddle-node, Hopf, Bogdanov-Takens, and Bautin. A reduced model via quasi-steady-state approximation (QSSA) is also proposed, preserving the core dynamic structure to facilitate bifurcation analysis. A central finding of our study is the critical role of the monocyte-mediated T cell activation rate, denoted by the parameter $\beta$ , which encapsulates the immunostimulatory potential of inflammatory monocytes presenting tumor antigens via MHCI cross-dressing. Numerical continuation corroborates the existence of multiple codimension-two organizing centers, delineating parameter regimes of tumor clearance, immune-mediated control, bistability, sustained oscillations, and inevitable escape. Our results quantitatively characterize the critical role of the monocyte-T-cell activation rate ( $\beta$ ) and the Allee threshold ( $\gamma$ ) in tipping the balance between immune surveillance and tumor persistence. This framework provides actionable bifurcation-based criteria for designing combination immunotherapies that enhance antigen presentation or monocyte functionality to shift the system toward tumor-eliminating attractors.

Calibrating mathematical models of biological processes is essential for achieving predictive accuracy and gaining mechanistic insight. However, this task remains challenging due to limited and noisy data, significant biological variability, and the computational complexity of the models themselves. In this method's article, we explore a range of approaches for parameter inference in partial differential equation (PDE) models of biological systems. We introduce a unified mathematical framework, the Correlation Integral Likelihood (CIL) method, for parameter estimation in systems exhibiting heterogeneous or chaotic dynamics, encompassing both pattern formation models and individual-based models. Departing from classical Bayesian inverse problem methodologies, we motivate the development of the CIL method, demonstrate its versatility, and highlight illustrative applications within mathematical biology. Furthermore, we compare stochastic sampling strategies, such as Markov Chain Monte Carlo (MCMC), with deterministic gradient flow approaches, highlighting how these methods can be integrated within the proposed framework to enhance inference performance. Our work provides a practical and theoretically grounded toolbox for researchers seeking to calibrate complex biological models using incomplete, noisy, or heterogeneous data, thereby advancing both the predictive capability and mechanistic understanding of such systems.