Journal of Mathematical Biology最新文献

Ranked tree-child networks are a recently introduced class of rooted phylogenetic networks in which the evolutionary events represented by the network are ordered so as to respect the flow of time. This class includes the well-studied ranked phylogenetic trees (also known as ranked genealogies). An important problem in phylogenetic analysis is to define distances between phylogenetic trees and networks in order to systematically compare them. Various distances have been defined on ranked binary phylogenetic trees, but very little is known about comparing ranked tree-child networks. In this paper, we introduce an approach to compare binary ranked tree-child networks on the same leaf set that is based on a new encoding of such networks that is given in terms of a certain partially ordered set. This allows us to define two new spaces of ranked binary tree-child networks. The first space can be considered as a generalization of the recently introduced space of ranked binary phylogenetic trees whose distance is defined in terms of ranked nearest neighbor interchange moves. The second space is a continuous space that captures all equidistant tree-child networks and generalizes the space of ultrametric trees. In particular, we show that this continuous space is a so-called CAT(0)-orthant space which, for example, implies that the distance between two equidistant tree-child networks can be efficiently computed.

It is widely recognized that reciprocal interactions between cells and their microenvironment, via mechanical forces and biochemical signaling pathways, regulate cell behaviors during normal development, homeostasis and disease progression such as cancer. However, how exactly cells and tissues regulate growth in response to chemical and mechanical cues is still not clear. Here, we propose a framework for the chemomechanical regulation of growth based on thermodynamics of continua and growth-elasticity to predict growth patterns. Combining the elastic and chemical energies, we use an energy variational approach to derive a novel formulation that isolates the mass-conserving tissue rearrangement from the mass-accretion volumetric growth, and incorporates independent energy-dissipating stress relaxation and biochemomechanical regulation of the volumetric growth rate respectively. We validate the model using experimental data from growth of tumor spheroids in confined environments. We also investigate the influence of model parameters, including tissue rearrangement rate, tissue compressibility, strength of mechanical feedback and external mechanical stimuli, on the growth patterns of tumor spheroids.

Complex contagion models that involve contagion along higher-order structures, such as simplicial complexes and hypergraphs, yield new classes of mean-field models. Interestingly, the differential equations arising from many such models often exhibit a similar form, resulting in qualitatively comparable global bifurcation patterns. Motivated by this observation, we investigate a generalised mean-field-type model that provides a unified framework for analysing a range of different models. In particular, we derive analytical conditions for the emergence of different bifurcation regimes exhibited by three models of increasing complexity-ranging from three- and four-body interactions to two connected populations which simultaneously includes both pairwise and three-body interactions. For the first two cases, we give a complete characterisation of all possible outcomes, along with the corresponding conditions on network and epidemic parameters. In the third case, we demonstrate that multistability is possible despite only three-body interactions. Our results reveal that single population models with three-body interactions can only exhibit simple transcritical transitions or bistability, whereas with four-body interactions multistability with two distinct endemic steady states is possible. Surprisingly, the two-population model exhibits multistability via symmetry breaking despite three-body interactions only. Our work sheds light on the relationship between equation structure and model behaviour and makes the first step towards elucidating mechanisms by which different system behaviours arise, and how network and dynamic properties facilitate or hinder outcomes.

Many animals show avoidance behavior in response to disease. For instance, in some species of frogs, individuals that survive infection of the fungal disease chytridiomycosis may learn to avoid areas where the pathogen is present. As chytridiomycosis has caused substantial declines in many amphibian populations worldwide, it is a highly relevant example for studying these behavioral dynamics. Here we develop compartmental ODE models to study the epidemiological consequences of avoidance behavior of animals in response to waterborne infectious diseases. Individuals with avoidance behavior are less likely to become infected, but avoidance may also entail increased risk of mortality. We compare the outbreak dynamics with avoidance behavior that is innate (present from birth) or learned (gained after surviving infection). We also consider how management to induce learned avoidance might affect the resulting dynamics. Using methods from dynamical systems theory, we calculate the basic reproduction number [Formula: see text] for each model, analyze equilibrium stability of the systems, and perform a detailed bifurcation analysis. We show that disease persistence when [Formula: see text] is possible with learned avoidance, but not with innate avoidance. Our results imply that management to induce behavioral avoidance can actually cause such a scenario, but it is also less likely to occur for high-mortality diseases (e.g., chytridiomycosis). Furthermore, the learned avoidance model demonstrates a variety of codimension-1 and -2 bifurcations not found in the innate avoidance model. Simulations with parameters based on chytridiomycosis are used to demonstrate these features and compare the outcomes with innate, learned, and no avoidance behavior.

The aggregation and accumulation of oligomers of misfolded Aβ-amyloids in the human brain is one of the possible causes for the onset of the Alzheimer's disease in the early stage. We introduce and study a new ODE model for the evolution of Alzheimer's disease based on the interaction between monomers, proto-oligomers, and oligomers of Aβ amyloid protein in a small portion of the human brain, based upon biochemical processes such as polymerization, depolymerization, fragmentation and concatenation. We further introduce the possibility of controlling the evolution of the system via a treatment that targets the monomers and/or the oligomers. We observe that a combined optimal treatment on both monomers and oligomers induces a substantial decrease of the oligomer concentration at the final stage. A single treatment on oligomers performs better than a single treatment on monomers. These results shed a light on the effectiveness of immunotherapy using anti-Aβ antibodies, targeting monomers or oligomers. Several numerical simulations show how the oligomer concentration evolves without treatment, with single monomer/oligomer treatment, or with a combined treatment.

This paper is a follow-up to a previous work where we considered populations with time-varying growth rates living in patches and irreducible migration matrix between the patches. Each population, when isolated, would become extinct. Dispersal-induced growth (DIG) occurs when the populations are able to persist and grow exponentially when dispersal among the populations is present. In this paper, we consider the situation where the migration matrix is not necessarily irreducible. We provide a mathematical analysis of the DIG phenomenon, in the context of a deterministic model with periodic variation of growth rates and migration. Our results apply in the case, important for applications, where there is migration in one direction in one season and in the other direction in another season. We also consider dispersal-induced decay (DID), where each population, when isolated, grows exponentially, while populations die out when dispersal between populations is present.

In order to be useful in assessing the effects of climate change on biological populations, mathematical models have to adequately represent the life cycle of the species in question, the dynamics of and interactions with its resource(s), and the effect of changing environmental conditions on their vital rates. Due to this complexity, such models are often analytically intractable. We present here a consumer-resource model that captures seasonality (summer and winter), with synchronously reproducing consumers (birth pulse), structured into non-reproductive juveniles and reproductive adults, and that remains analytically tractable. Our model is motivated by hibernating mammals, such as marmots, ground squirrels, or bats, some of which live in high altitude regions where the effects of climate change are stronger than elsewhere. One stage-specific impact of climate change in those species is that juveniles may benefit from warmer winters while adults may suffer. We explore various aspects of how this differential response to climate change shapes population dynamics from stable populations to cycles and chaos. We show that the qualitative relationship between winter temperature and winter mortality has a significant effect on the model dynamics, hence informing empiricists of required data to assess the effect of climate change on these species. Our results question the long-standing expectation that species with slower life histories are necessarily more strongly affected by climate change than species with faster life histories.

The complex and dynamic crosstalk between tumour and immune cells results in tumours that can exhibit distinct qualitative behaviours-elimination, equilibrium, and escape-and intricate spatial patterns, yet share similar cell configurations in the early stages. We offer a topological approach to analyse time series of spatial data of cell locations (including tumour cells and macrophages) in order to predict malignant behaviour. We propose four topological vectorisations specialised to such cell data: persistence images of Vietoris-Rips and radial filtrations at static time points, and persistence images for zigzag filtrations and persistence vineyards varying in time. To demonstrate the approach, synthetic data are generated from an agent-based model with varying parameters. We compare the performance of topological summaries in predicting-with logistic regression at various time steps-whether tumour niches surrounding blood vessels are present at the end of the simulation, as a proxy for metastasis (i.e., tumour escape). We find that both static and time-dependent methods accurately identify perivascular niche formation, significantly earlier than simpler markers such as the number of tumour cells and the macrophage phenotype ratio. We find additionally that dimension 0 persistence applied to macrophage data, representing multi-scale clusters of the spatial arrangement of macrophages, performs best at this classification task at early time steps, prior to full tumour development, and performs even better when time-dependent data are included; in contrast, topological measures capturing the shape of the tumour, such as tortuosity and punctures in the cell arrangement, perform best at intermediate and later stages. We analyse the logistic regression coefficients for each method to identify detailed shape differences between the classes.

We study a reaction-diffusion system involving two species competing in temporally periodic and spatially heterogeneous environments. In this system, the species move horizontally and vertically with different probabilities, which can be regarded as dispersal strategies. The selection mechanisms in this case are more intricate than those observed in random diffusion scenarios. We investigate the stability of the semi-trivial periodic solutions in terms of the sign of the principal eigenvalue associated with a linear periodic eigenvalue problem. Furthermore, we provide sufficient conditions for the coexistence of two species. Additionally, numerical simulations are performed to facilitate further research and exploration.