Bulletin of Mathematical Biology最新文献

The use of ad-hoc engineered viruses in the fight against tumours is one of the greatest ideas in cancer therapeutics within the last three decades. Although some remarkable successes have been obtained, it is still not entirely clear how to achieve reliable protocols that can be routinely employed with confidence on a significant range of tumours. In this work, we concentrate on the study of different mathematical descriptions of virotherapy with the aim of better understanding the role of viral infectivity and viral dynamics in positive therapeutic outcomes. In particular, we compare probabilistic, individual approaches with continuous, spatially inhomogeneous models and investigate the importance of different tumour motility and different mathematical representations of viral infectivity. Some of these formulations also allow us to arrive at better analytical characterisation of how waves of viral infections arise and propagate in tumours, providing interesting insights into therapy dynamics. Similarly to previous studies, oscillatory behaviours, stochasticity and cancers' diffusivities are all central to the eradication or the escape of tumours under virotherapy. Here, though, our results also show that the ability of viruses to infect tumours seems, in certain cases, more important to a final positive outcome than tumours' motility or even reproductivity. This could hopefully represent a first step into better insights into viral dynamics that may help clinicians to achieve consistently better outcomes.

Chimeric antigen receptor (CAR) T cell therapy has shown remarkable success in hematological malignancies, yet patient responses remain highly variable and the roles of CD4⁺ and CD8⁺ subsets are not fully understood. We present an extended mathematical framework of CAR-T cell dynamics that explicitly models CD4⁺ helper and CD8⁺ cytotoxic lineages and their interactions with tumor antigen burden. Building on a recent model of antigen-regulated memory-effector-exhaustion transitions in CAR-T cells, our system of differential equations incorporates CD4⁺-mediated modulation of CD8⁺ proliferation, cytotoxicity, and memory regeneration through biologically grounded, saturating interactions. Sensitivity analyses identify effector proliferation, antigen turnover, and CD8⁺ expansion rates as dominant drivers of treatment outcome. Virtual patient simulations recover reported qualitative trends in CAR-T composition, including enhanced expansion and tumor clearance for defined CD4:CD8 products relative to CD8-only formulations, while also revealing inter-patient variability and time-dependent effects. To assess the practical limits of patient-level prediction under parameter uncertainty, we introduce controlled noise into key parameters and show that direct mechanistic classification rapidly degrades. We then demonstrate that a simple feed-forward neural network can partially recover predictive signal from noisy inputs, outperforming a naïve baseline while remaining consistent with mechanistic sensitivities. This work positions the extended model as a hypothesis generator, and illustrates how data-driven methods can complement mechanistic modeling when parameter uncertainty constrains predictive confidence.

In the classic SIR model, infection gives full immunity against any possible reinfection. However, for many important epidemiological situations, immunity is only partial and reinfection is possible. Though these models are mathematically more complex, we are able to find expressions for the epidemic final size. We also generalise these expressions to include vaccination, with a fraction of the population vaccinated before the epidemic, where vaccinees are less susceptible to primary infections than unvaccinated hosts.Partial immunity can be interpreted at the population level as providing either full or no protection to each host, in some proportion (all-or-none immunity). In this scenario, we give analytical expressions (mathematically similar to the SIR final-size) for the cumulative primary infections and the cumulative reinfections in unvaccinated and vaccinated hosts. Alternatively, partial immunity can be interpreted as providing homogeneous imperfect protection to each host (leaky immunity). For this other scenario, we again obtain an implicit equation for the final epidemic size. We break down, in terms of the final size, the number of infections in hosts with or without prior immunity (vaccine- or infection- induced), as well as the number of primary infections and reinfections. Under the leaky immunity assumption, we find a form of reinfection threshold. If the relative host susceptibility to reinfection is above this threshold (which is the inverse of the pathogen's basic reproduction number), transmission rates are high enough to support an endemic disease. Below the reinfection threshold, epidemics are transient. In the all-or-none model, epidemics are always transient.

We extend the formulation of a non-local PDE model of collective cell migration involving attracting or repelling cellular interactions to the case of time-dependent spatial domains as present, for instance, in modelling developmental processes from embryology. We restrict to a spatially one-dimensional setting, as is appropriate for the modelling of neural crest cell invasion, and focus on the case of spatially homogeneous domain change as this already highlights many of the modelling and numerical challenges. The approach is illustrated and numerical simulations are presented and discussed for a model of an aggregating cellular population and for a simple model of neural crest cell invasion accounting for contact inhibition of locomotion.

The global spread of the Zika virus (ZIKV), compounded by the absence of effective antiviral drugs or widely available vaccines, highlights the importance of understanding its transmission dynamics to implement effective public health strategies. The transmission of the Zika virus is attributable to the heterogeneity of sexual contacts and the lack of miracle drugs or vaccines. We develop a degree-based mathematical network model which takes account of heterogeneity of sexual contacts and the adoption of preventive measures. We derive analytical expressions for the basic reproduction number for three scenarios: mosquito-borne transmission only, sexual transmission only, and a combined scenario where both transmission routes coexist. In particular, we demonstrate that the basic reproduction number is proportional to the degree of network heterogeneity when the Zika virus transmission is solely driven by sexual contacts. Our proposed model possesses infinitely many disease-free equilibrium points, and we prove that these collectively form a locally attracting set under specified conditions. Finally, we present numerical simulations, calibrated with Zika epidemic data from Brazil (2015-2016), which indicate that increasing the number of individuals who take comprehensive protective measures (using screens, mosquito nets, insect repellent, condoms, etc.) can significantly reduce the final epidemic size.

Phylogenetic networks are an important way to represent evolutionary histories that involve reticulate processes such as hybridisation or horizontal gene transfer, yet fundamental questions such as how many networks there are that satisfy certain properties are very difficult. A new way to encode a large class of networks, using "expanding covers", may provide a way to approach such problems. Expanding covers encode a large class of phylogenetic networks, called labellable networks. This class does not include all networks, but does include many familiar classes, including orchard, normal, tree-child and tree-sibling networks. As expanding covers are a combinatorial structure, it is possible that they can be used as a tool for counting such classes for a fixed number of leaves and reticulations, for which, in many cases, a closed formula has not yet been found. More recently, a new class of networks was introduced, called spinal networks, which are analogous to caterpillar trees for phylogenetic trees and can be fully described using covers. In the present article, we describe a method for counting networks that are both spinal and belong to some more familiar class, with the hope that these form a base case from which to attack the more general classes.

As part of work to connect phylogenetics with machine learning, there has been considerable recent interest in vector encodings of phylogenetic trees. We present a simple new "ordered leaf attachment" (OLA) method for uniquely encoding a binary, rooted phylogenetic tree topology as an integer vector. OLA encoding and decoding take linear time in the number of leaf nodes, and the set of vectors corresponding to trees is a simply-described subset of integer sequences. The OLA encoding is unique compared to other existing encodings in having these properties. The integer vector encoding induces a distance on the set of trees, and we investigate this distance in relation to the NNI and SPR distances.

Kinetic modeling of microbial growth is essential for the design, optimization, and scale-up of industrial bioprocesses. Classical empirical models often lack biologically interpretable parameters or fail to capture complex multiphasic (polyauxic) behaviors, while fully mechanistic models are impractical for systems involving complex substrates and mixed cultures. This study proposes a unified mathematical framework that reformulates the canonical Boltzmann and Gompertz equations into semi-mechanistic forms, explicitly defining the maximum specific reaction rate and lag phase duration. Polyauxic growth is represented as a weighted sum of sigmoidal phases, subject to stringent constraints that ensure parameter identifiability, temporal consistency, and biological plausibility. The methodology integrates a workflow to address nonlinear regression in high-dimensional parameter spaces. A two-stage optimization strategy using Differential Evolution for global search followed by L-BFGS-B for local refinement avoid bias and heuristic parameter initialization. A Charbonnier loss function and the Robust Regression and Outlier Removal procedure are employed to identify and mitigate experimental outliers. Model parsimony is enforced using Akaike (AIC, AICc) and Bayesian (BIC) information criteria to select the optimal number of growth phases and avoid overparameterization. The framework was evaluated using experimental anaerobic digestion datasets, demonstrating that conventional single-phase models can obscure relevant metabolic transitions in co-digestion systems.

Cell size is a fundamental determinant of cellular physiology, influencing processes such as growth, division, and function. In this study, we develop a segmented mathematical framework to investigate how different control mechanisms operating across multiple phases of the cell cycle affect fibroblast population dynamics. Building on our previous work modeling sizer, timer, and adder strategies, we extend the analysis by introducing phase-specific control schemes in the S and G2 phases, incorporating nonlinear growth dynamics and cell death. Using agent-based stochastic simulations, we examine how these mechanisms shape steady-state size distributions and respond to parameter variations. Our results reveal that the steady-state cell size distribution is primarily governed by division kernels and phase-specific control strategies, and appears remarkably robust to cell death modalities. We identify a fundamental trade-off between extrinsic and intrinsic growth feedbacks: while population-density-dependent regulation tightly limits total cell numbers, cell-size-dependent regulation acts as a proportional homeostatic mechanism, suppressing relative size variability. Furthermore, we demonstrate that population recovery is accelerated by the retention of proliferation-competent large cells. This study provides biologically relevant insights into the complex interplay between growth, division, and homeostasis, with implications for understanding tissue repair and disease progression.