Journal of Mathematical Biology最新文献

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.

Intratumour phenotypic heterogeneity is understood to play a critical role in disease progression and treatment failure. Accordingly, there has been increasing interest in the development of mathematical models capable of capturing its role in cancer cell adaptation. This can be systematically achieved by means of models comprising phenotype-structured nonlocal partial differential equations, tracking the evolution of the phenotypic density distribution of the cell population, which may be compared to gene and protein expression distributions obtained experimentally. Nevertheless, given the high analytical and computational cost of solving these models, much is to be gained from reducing them to systems of ordinary differential equations for the moments of the distribution. We propose a generalised method of model-reduction, relying on the use of a moment generating function, Taylor series expansion and truncation closure, to reduce a nonlocal reaction-advection-diffusion equation, with general phenotypic drift and proliferation rate functions, to a system of moment equations up to arbitrary order. Our method extends previous results in the literature, which we address via three examples, by removing any a priori assumption on the shape of the distribution, and provides a flexible framework for mathematical modellers to account for the role of phenotypic heterogeneity in cancer adaptive dynamics, in a simpler mathematical framework.

The Tallis-Leyton model is a simple model of parasite acquisition where parasites accumulate in the host without affecting the host's mortality, or eliciting any immune reaction from the host. Furthermore, the parasites do not reproduce in the host. We examine how the variability in parasite loads among hosts is affected by the rate of infectious contacts, the distribution of parasite entering the host during infectious contacts, the host's age, and the distribution of parasite lifetimes. Motivated by empirical studies in parasitology, variability is examined in the sense of the Lorenz order and related metrics. Perhaps counterintuitively, increased variability in the distribution of parasite lifetimes is seen to decrease variability in the parasite loads among hosts.