Bulletin of Mathematical Biology最新文献

Phylogenetic trees are simple models of evolutionary processes. They describe conditionally independent divergent evolution from common ancestors. However, they often lack the flexibility to represent processes like introgressive hybridization, which leads to gene flow between taxa. Phylogenetic networks generalize trees but typically assume that ancestral taxa merge instantaneously to form "hybrid" descendants. In contrast, convergence-divergence models retain a single underlying "principal tree" and permit gene flow over arbitrary time frames. They can also model other biological processes leading to taxa becoming more similar, such as replicated evolution. We present novel maximum likelihood algorithms to infer most aspects of N-taxon convergence-divergence models - many consistently - using a quartet-based approach. All algorithms use 4-taxon convergence-divergence models, inferred from subsets of the N taxa using a model selection criterion. The first algorithm infers an N-taxon principal tree; the second infers sets of converging taxa; and the third infers model parameters - root probabilities, edge lengths and convergence parameters. The algorithms can be applied to multiple sequence alignments restricted to genes or genomic windows or to gene presence/absence datasets. We demonstrate that convergence-divergence models can be accurately recovered from simulated data.

Breast cancer brain metastases (BCBM) affect nearly 90,000 patients annually in the United States and carry a significant risk of mortality. As metastatic lesions develop, the unique milieu of the brain microenvironment shapes disease progression and therapeutic response. Among resident brain cells, astrocytes are both the most common, and are increasingly recognized as key regulators of this process, yet their precise role remains poorly defined. Here, we present a hybrid agent-based model (ABM) to simulate tumor-astrocyte interactions on a two-dimensional lattice. In our model, metastatic tumor cells induce phenotypic reprogramming of astrocytes from an anti- to a pro-metastatic state, thereby enhancing tumor proliferation. We systematically evaluate how variations in astrocyte density, spatial distribution, and chemotherapy impact tumor expansion and spatial morphology, quantified by fractal dimension, lacunarity, and eccentricity. Our simulations reveal that astrocyte reprogramming accelerates tumor progression and contributes to increased morphological complexity and chemotherapeutic resistance.

Epidemics are nonlinear adaptive processes in which pathogen spread and human behavior form a tightly coupled feedback loop. Individual decisions about protective measures create strategic interactions. These interactions can either accelerate disease spread or drive collective suppression. We introduce a theoretical lattice-based agent model that fuses SIS contagion with an evolutionary game, systematically exploring how strategy choice and infection pressure co-evolve through comprehensive parameter space analysis. Agents choose between self-isolation and normal activity based on population-wide disease prevalence and perceived costs. Agents then update strategies using a Fermi rule based on global infection prevalence and perceived costs. Infections propagate through contact-based transmission with behavior-dependent probability. We model transmission with a hierarchical probability structure where cross-infection coupling captures risk at behavioral interfaces between strategies. Comprehensive exploration of the four-dimensional parameter space reveals sharp phase transitions between cooperative and defective regimes. These transitions are governed by transmission intensity, recovery probability, risk perception, and economic pressures. A striking paradox emerges: while intense cross-infection coupling drives near-universal isolation adoption, it paradoxically sustains persistent endemic infection, demonstrating that widespread cooperation does not guarantee epidemic control. Modest changes in isolation costs or cross-infection coupling trigger complete phase inversions. This extreme sensitivity characterizes systems operating near critical points. Contact-mediated spread generates persistent spatial patterning in infection status and compartment composition. These findings establish epidemic-behavioral coupling as a fundamentally nonlinear dynamical system exhibiting critical phenomena and emergent spatial organization. Cooperation emergence does not guarantee epidemic control, revealing complex theoretical relationships between individual decision-making and collective health outcomes that require empirical validation for practical application.

Changes in environmental or system parameters often drive major biological transitions, including ecosystem collapse, disease outbreaks, and tumor development. Analyzing the stability of steady states in dynamical systems provides critical insight into these transitions. This paper introduces an algebraic framework for analyzing the stability landscapes of ecological models defined by systems of first-order autonomous ordinary differential equations with polynomial or rational rate functions. Using tools from real algebraic geometry, we characterize parameter regions associated with steady-state feasibility and stability via three key boundaries: singular, stability (Routh-Hurwitz), and coordinate boundaries. With these boundaries in mind, we employ routing functions to compute the connected components of parameter space in which the number and type of stable steady states remain constant, revealing the stability landscape of these ecological models. As case studies, we revisit the classical Levins-Culver competition-colonization model and a recent model of coral-bacteria symbioses. In the latter, our method uncovers complex stability regimes, including regions supporting limit cycles, that are inaccessible via traditional techniques. These results demonstrate the potential of our approach to inform ecological theory and intervention strategies in systems with nonlinear interactions and multiple stable states.

This work addresses multistationarity of fully open reaction networks equipped with mass action kinetics. We improve upon existing results relating existence of positive feedback loops in a reaction network and multistationarity; and we provide a novel deterministic operation to generate new non-multistationary networks. This is interesting because while there were many operations to create infinitely many new multistationary networks from a multistationary example, this is the first such operation for the non-multistationary counterpart. Such tools for the generation of example networks have a use-case in the application of data science to reaction network theory. We demonstrate this by using new data, along with a novel graph representation of reaction networks that is unique up to a permutation on the name of species of the network, to train a graph attention neural network model to predict multistationarity of reaction networks. This is the first time machine learning tools are used for studying classification problems of reaction networks.

Mathematical oncology is an interdisciplinary research field where the mathematical sciences meet cancer research. Being situated at the intersection of these two fields makes mathematical oncology highly dynamic, as practicing researchers are incentivised to quickly adapt to both technical and medical research advances. Determining the scope of mathematical oncology is therefore not straightforward; however, it is important for purposes related to funding allocation, education, scientific communication, and community organisation. To address this issue, we here conduct a bibliometric analysis of mathematical oncology. We compare our results to the broader field of mathematical biology, and position our findings within theoretical science-of-science frameworks. Based on article metadata and citation flows, our results provide evidence that mathematical oncology has undergone a significant evolution since the 1960s marked by increased interactions with other disciplines, geographical expansion, larger research teams, and greater diversity in studied topics. The latter finding contributes to the greater discussion on which models different research communities consider to be valuable in the era of big data and machine learning. Further, the results presented in this study quantitatively motivate that international collaboration networks should be supported to enable new countries to enter and remain in the field, and that mathematical oncology benefits both mathematics and the life sciences.

The Colijn-Plazzotta ranking is a bijective encoding of the unlabeled binary rooted trees with positive integers. We show that the rank f(t) of a tree t is closely related to its height h, the maximal path length from a leaf to the root. We consider the rank $f\left({\tau }_n\right)$ of a random n-leaf tree ${\tau }_n$ under each of three models: (i) uniformly random unlabeled unordered binary rooted trees, or unlabeled topologies; (ii) uniformly random leaf-labeled binary trees, or labeled topologies under the uniform model; and (iii) random binary search trees, or labeled topologies under the Yule-Harding model. Relying on the close relationship between tree rank and tree height, we obtain results concerning the asymptotic properties of $loglogf\left({\tau }_n\right)$ . In particular, we find $E\{{log}_{2}logf\left({\tau }_n\right)\}\sim 2\sqrt{\pi n}$ for uniformly random unlabeled ordered binary rooted trees and uniformly random leaf-labeled binary trees, and for a constant $\alpha \approx 4.31107$ , $E\{{log}_{2}logf\left({\tau }_n\right)\}\sim \alpha logn$ for leaf-labeled binary trees under the Yule-Harding model. We show that the mean of $f\left({\tau }_n\right)$ itself under the three models is largely determined by the rank $c_{n-1}$ of the highest-ranked tree-the caterpillar-obtaining an asymptotic relationship with ${\pi }_n{c}_{n-1}$ , where ${\pi }_n$ is a model-specific function of n. The results resolve open problems, providing a new class of results on an encoding useful in mathematical phylogenetics.

A central challenge in Human Immunodeficiency Virus (HIV) public health policy lies in determining whether to universally expand treatment access, despite the risk of sub-optimal adherence and consequent drug resistance, or to adopt a more strategic allocation of resources that balances treatment coverage with adherence support. This dilemma is further complicated by the need for timely switching to second-line therapy, which is critical for managing treatment failure but imposes additional burdens on limited healthcare resources. In this study, we develop and analyze a compartmental model of HIV transmission that incorporates both drug-sensitive and drug-resistant strains, diagnosis status, and treatment progression, including switching to second-line therapy upon detection of resistance. Basic reproduction numbers for both strains are derived, and equilibrium analysis reveals the existence of a disease-free state and two endemic states, where the drug-sensitive strain may be eliminated while the drug-resistant strain persists. Local and global sensitivity analyses are performed, using partial rank correlation coefficient (PRCC) and Sobol methods, to identify key parameters influencing different model outcomes. We extend the model using optimal control theory to assess multiple intervention strategies targeting diagnosis, treatment initiation, and adherence. A novel dynamic control framework is proposed to achieve the UNAIDS 95-95-95 targets through efficient resource allocation. Numerical simulations validate the analytical results and compare the effectiveness and cost-efficiency of control strategies. Our findings highlight that long-term HIV epidemic control depends critically on prioritizing adherence-focused interventions alongside efforts to expand first-line treatment coverage.

The application of non-steroidal anti-inflammatory drugs (NSAIDs) for Alzheimer's disease is considered to be a promising therapeutic approach. Epidemiological studies suggest potential benefits of NSAIDs; however, these findings are not consistently supported by clinical trials. This long-standing discrepancy has persisted for decades and remains a significant barrier to developing effective treatment strategies. To assess the efficacy of NSAIDs in Alzheimer's disease, we have developed a mathematical model based on a system of ordinary differential equations. The model captures the dynamics of key players in disease progression, including A $\beta$ -monomers, oligomers, pro-inflammatory mediators (M1 microglial cells and pro-inflammatory cytokines), and anti-inflammatory mediators (M2 microglial cells and anti-inflammatory cytokines). The effects of NSAIDs are modeled through a reduction in the production rate of inflammatory cytokines (IC). While a single NSAID administration temporarily reduces IC levels, their concentration eventually returns to baseline due to drug elimination. The return time depends on the drug dose, resulting in a patient-specific return time function. By analyzing this function, we propose an optimal treatment regimen and identify conditions under which NSAID treatment is most effective in reducing IC levels. Our results suggest that NSAID efficacy in Alzheimer's disease is influenced by the stage of the disease (with earlier intervention being more effective), patient-specific parameters, and the treatment regimen. The approach developed here can also be generalized to evaluate the efficacy of anti-inflammatory treatments for other diseases.