Bulletin of Mathematical Biology最新文献

Phylogenetic networks describe the evolution of a set of taxa for which reticulate events have occurred at some point in their evolutionary history. Of particular interest is when the evolutionary history between a set of just three taxa has a reticulate event. In molecular phylogenetics, substitution models can model the process of evolution at the genetic level, and the case of three taxa with a reticulate event can be modeled using a substitution model on a semi-directed graph called a 3-sunlet. We investigate a class of substitution models called group-based phylogenetic models on 3-sunlet networks. In particular, we investigate the discrete geometry of the parameter space and how this relates to the dimension of the phylogenetic variety associated to the model. This enables us to give a dimension formula for this variety for general group-based models when the order of the group is odd.

This study examines a competition model featuring nonuniform dispersal, referred to as starvation-driven-type diffusion (SDTD). This model incorporates the motility of species that adhere to a starvation-driven diffusion (SDTD). paradigm while also factoring in perceptual constraints within a spatially heterogeneous region. In the proposed model, our study aims to understand the impact of SDTD on system dynamics in a spatially heterogeneous environment. To achieve this, we consider a Lotka-Volterra-type competition model exhibiting identical population dynamics under no-flux boundary conditions. To illuminate the evolutionary implications of SDTD, this study contrasts two different models. The first model involves two species with distinct, uniform diffusion rates. In comparison, the second model features one species that adheres to a constant diffusion rate and another that operates under the principles of SDTD. This study focuses on analyzing the fitness variation of competing species based on their respective diffusion dynamics: (i) The study examines how the fitness of a species following SDTD changes compared to another species that diffuses at a constant rate. (ii) We investigate the dynamics of fitness alteration within a competitive two-species model wherein one species exhibits a constant diffusion rate while the other species alternates between constant-rate diffusion and SDTD. In addition, we examine how the shifting diffusion strategies of one species affect its fitness relative to a species with a fixed, constant diffusion rate. Our conclusions suggest that a species adhering to SDTD may enhance its fitness, consistent with the model incorporating SDD. Nonetheless, we show that certain circumstances may exist where SDTD does not result in increased fitness for a species, mainly due to the perceptual limitations of that species.

This study examines influenza transmission dynamics through mathematical modeling, vaccination strategies using optimal control, and the impact of key model parameters to the optimal control for the 2023-2024 influenza season in the United States. Using data from the CDC's FluView Interactive and FluVaxView databases, key parameters were estimated, revealing significant variability across states. Tailored vaccination strategies, designed to align with state-specific data and conditions, effectively reduced infections and reproduction numbers in all states. Sensitivity analysis of the optimal vaccination strategy and reproduction number revealed complex interactions among model parameters. These findings emphasize the need for carefully designed public health strategies to manage influenza effectively, supported by key recommendations presented in this paper.

Coral reefs are increasingly subjected to major disturbances threatening the health of marine ecosystems. Substantial research is underway to develop intervention strategies that assist reefs in recovery from, and resistance to, inevitable future climate and weather extremes. To assess potential benefits of interventions, mechanistic understanding of coral reef recovery and resistance patterns is essential. Recent evidence suggests that more than half of the reefs surveyed across the Great Barrier Reef (GBR) exhibit deviations from standard recovery modelling assumptions when the initial coral cover is low ( $\le 10$ %). New modelling is necessary to account for these observed patterns to better inform management strategies. We consider a new model for reef recovery at the coral cover scale that accounts for biphasic recovery patterns. The model is based on a multispecies Richards' growth model that includes a change point in the recovery patterns. Bayesian inference is applied for uncertainty quantification of key parameters for assessing reef health and recovery patterns. This analysis is applied to benthic survey data from the Australian Institute of Marine Science (AIMS). We demonstrate agreement between model predictions and data across every recorded recovery trajectory with at least two years of observations following disturbance events occurring between 1992-2020. This new approach will enable new insights into the biological, ecological and environmental factors that contribute to the duration and severity of biphasic coral recovery patterns across the GBR. These new insights will help to inform managements and monitoring practice to mitigate the impacts of climate change on coral reefs.

Chronic antigen exposure in the tumor microenvironment drives CD $8^{+}$ T cell exhaustion, marked by increased inhibitory receptors and diminished effector functions. Immune checkpoint blockade seeks to prevent or reverse exhaustion, but its success relies on the pre-existing state of tumor-infiltrating T cells. To investigate this, we developed a mathematical model examining: (1) how T cell exhaustion disrupts tumor-immune equilibrium, (2) anti-PD-L1 efficacy across exhaustion states, and (3) efficacy of next-generation therapies (e.g., IFN $\alpha$ -anti-PD-L1, PD1-IL2v). Stability analysis and simulations reveal that tumor PD-L1 expression critically influences immune dynamics, particularly the bistability of tumor-free and tumorous states. High PD-1 expression and exhaustion rates correlate with growth of tumor and impaired expansion of less-exhausted CD $8^{+}$ T cells. While anti-PD-L1 efficacy depends on baseline exhaustion, severe exhaustion enables immune escape. Next-generation therapies enhancing cytotoxicity and sustaining less-exhausted T cell populations show improved tumor control, suggesting combination strategies may overcome resistance.

Autoimmune myocarditis, or cardiac muscle inflammation, is a rare but frequently fatal side-effect of immune checkpoint inhibitors (ICIs), a class of cancer therapies. Despite the dangers that side-effects such as these pose to patients, they are rarely, if ever, included explicitly when mechanistic mathematical modelling of cancer therapy is used for optimization of treatment. In this paper, we develop a two-compartment mathematical model which incorporates the impact of ICIs on both the heart and the tumour. Such a model can be used to inform the conditions under which autoimmune myocarditis may develop as a consequence of treatment. We use this model in an optimal control framework to design optimized dosing schedules for three types of ICI therapy that balance the positive and negative effects of treatment. We show that including the negative side-effects of ICI treatment explicitly within the mathematical framework significantly impacts the predictions for the optimized dosing schedule, thus stressing the importance of a holistic approach to optimizing cancer therapy regimens.

Switch-like behavior and bistability are important features in gene regulatory networks, allowing cells to distinguish between changing environments and express certain genes only under the appropriate conditions. Vibrio vulnificus, an opportunistic Gram-negative marine pathogen, has iron as a limiting growth factor. When inside a human host, this bacteria utilizes heme as a source of iron, necessitating the ability to turn this heme acquisition system off and on in response to environmental pressures. As establishment of infection depends on V. vulnificus's ability to change from a marine to human environment, the ability to switch on the heme-intake system is an important part of establishment of initial infection. In particular, the protein HupA is a key part of the bacteria's heme importation complex, and is regulated primarily by a divergently transcribed protein, HupR. The dynamics of this regulation result in a genetic switch, allowing the bacteria to differentiate between high iron or high heme environments, determining which source of iron should be used. Bifurcation analysis of this network uncovers a saddle-node bifurcation, which encodes this switch-like behavior into the regulation of the heme transport system and allows different levels of expression for HupA depending on external concentrations of heme and iron. The influences of other parameters in this system are also investigated; in particular, promoter leakage is found to be required to enable this bistability, indicating the importance of imperfect regulation in a cell's ability to respond to the environment.

Nonlocal perception plays a crucial role in studying animal cognitive movement modeling. In this paper, the impact of nonlocal perception on pattern formation is analyzed, and it is applied to study the control of pine wilt disease. It turns out that perceptual movement can provide a theoretical scientific basis for the multi-point outbreaks and spatiotemporal aggregation of pine wilt disease. For the top-hat kernel, we concentrate on the joint effect of perception scale and delay on the stability, and find that Turing-Hopf bifurcation occurs due to their interaction. Besides, the patterns near the bifurcation points are simulated in detail by adopting parameters with actual biological meaning, which are selected by analyzing real data, and diverse complicated spatiotemporal patterns are obtained, such as peak alternating periodic patterns and spatiotemporal aggregation patterns. Finally, we demonstrate that the artificial release of the parasitic natural enemy of the pest can drive the populations to reach stability in the form of the steady state or periodic solutions. The obtained results not only well explain the transmission mechanism of pine wilt disease, but also contribute to the study of biological phenomena such as the formations of flocks and swarms.

Collective cell migration plays a crucial role in numerous biological processes, including tumour growth, wound healing, and the immune response. Often, the migrating population consists of cells with various different phenotypes. This study derives a general mathematical framework for modelling cell migration in the local environment, which is coarse-grained from an underlying individual-based model that captures the dynamics of cell migration that are influenced by the phenotype of the cell, such as random movement, proliferation, phenotypic transitions, and interactions with the local environment. The resulting, flexible, and general model provides a continuum, macroscopic description of cell invasion, which represents the phenotype of the cell as a continuous variable and is much more amenable to simulation and analysis than its individual-based counterpart when considering a large number of phenotypes. We showcase the utility of the generalised framework in three biological scenarios: range expansion; cell invasion into the extracellular matrix; and T cell exhaustion. The results highlight how phenotypic structuring impacts the spatial and temporal dynamics of cell populations, demonstrating that different environmental pressures and phenotypic transition mechanisms significantly influence migration patterns, a phenomenon that would be computationally very expensive to explore using an individual-based model alone. This framework provides a versatile and robust tool for understanding the role of phenotypic heterogeneity in collective cell migration, with potential applications in optimising therapeutic strategies for diseases involving cell migration.

Aedes aegypti continues to cause many cases of dengue, chikungunya and Zika fever in affected areas of the tropical world. After being eradicated from Brazil in the decades of 1940 and 1950, Aedes aegypti returned with full force in the early 1970s. Knowing the total number of mosquitoes transmitting Aedes-borne infections is crucial for quantifying the intensity of transmission of these infections. In this paper, we propose a model to estimate the distribution of the number of Aedes mosquitoes' populations during an outbreak of either dengue or chikungunya. The model assumes that the mosquitoes' distribution follows a Gaussian Mesa Function (GMF), which has 5 parameters and allows for variable asymmetry. These 5 parameters are adjusted so that they fit indirectly, from a modified Ross‒Macdonald model, the incidence of dengue or chikungunya infections (see main text). Therefore, the observed incidence becomes a function of the parameters of the GMF. We illustrate the model with dengue and chikungunya data from 5 cities in the state of Minas Gerais in the southeastern region of Brazil for the 2023-2024 transmission season. The model shows that it is possible to estimate the size of the mosquitoes' population from incidence data, circumventing the logistic hurdles involved in the actual counting of mosquitoes. This is the most important practical contribution of this paper. The paper also contains several theoretical innovations, such as a modification of the Ross‒Macdonald model, which is usually presented for a constant mosquitoes' population, which, of course, is very unrealistic.