Journal of Mathematical Biology最新文献

This study is concerned with the global stability of positive equilibrium (PE) solutions in a juvenile-adult structured diffusive model featuring a mixed dispersal mechanism. Under certain generic assumptions, we establish the uniqueness and global stability of the PE. Moreover, we show that these assumptions hold if either (i) the population disperses slowly, or (ii) the adults' reproduction rate is large. In particular, our findings demonstrate that a high adult reproduction rate always benefits species survival. Interestingly, with elevated juvenile maturity rates, the population can face extinction if the average death rate of adults surpasses their average reproduction rate. A key aspect of our analysis involves deriving the exact asymptotic limit of the principal spectrum point of some cooperative systems with mixed dispersals with respect to specific model parameters. In addition, we conducted numerical simulations to illustrate our theoretical results.

This paper proposes a network-based framework to model and analyze the evolution and dynamics of a marine ecosystem. The model involves two different length scales: the evolution of species in local reserves and the exchange of species between reserves. At the inter-reserve level, species evolution is ruled by the replicator equation, while a transport function accounts for the transport at the network level. This multi-scale approach allows for capturing both local dynamics within individual reserves and the broader connectivity and interactions across the network. We study how equilibria are modified due to the exchange between connected nodes and prove that evolutionarily stable states are asymptotically stable if the velocity transfer $\nu$ is contained within a condition involving the maximum degree of the network. A fourth-order P-(EC) $_{}^k$ formulation of the Gauss-Legendre Runge Kutta scheme is adopted. This numerical procedure is challenged against a suitable numerical experiment involving three species on a single node for validating the robustness of the scheme in terms of accuracy for a large observation time. Several numerical experiments are provided for characterizing the abilities and limitations of the model. Three prototypical networks are considered for the case of two- and three-agent games with both linear and nonlinear transport terms. Moreover, the ability of the proposed model to reproduce synchronization phenomena on networks is discussed. This approach has been demonstrated to have the potential to uncover insights into the stability, resilience, and long-term behavior of these ecosystems, offering valuable tools for their conservation and management.

General conditions are established under which reaction-cross-diffusion systems can undergo spatiotemporal pattern-forming instabilities. Recent work has focused on designing systems theoretically and experimentally to exhibit patterns with specific features, but the case of non-diagonal diffusion matrices has yet to be analysed. Here, a framework is presented for the design of general n-component reaction-cross-diffusion systems that exhibit Turing and wave instabilities of a given wavelength. For a fixed set of reaction kinetics, it is shown how to choose diffusion matrices that produce each instability; conversely, for a given diffusion tensor, how to choose linearised kinetics. The theory is applied to several examples including a hyperbolic reaction-diffusion system, two different 3-component models, and a spatio-temporal version of the Ross-Macdonald model for the spread of malaria.

It has been noticed that when the waiting time distribution exhibits a transition from an intermediate time power-law decay to a long-time exponential decay in the continuous time random walk model, a transition from anomalous diffusion to normal diffusion can be observed at the population level. However, the mechanism behind the transition of waiting time distribution is rarely studied. In this paper, we provide one possible mechanism to explain the origin of such a transition. A stochastic model terminated by a state-dependent Poisson clock is studied by a formal asymptotic analysis for the time evolutionary equation of its probability density function (PDF). The waiting time behavior under a more relaxed setting can be rigorously characterized by probability tools. Both approaches show the transition phenomenon of the waiting time T, which is complemented by particle simulations to shed light on the transition time scale. Our results indicate that small drift relative to noise in the state equation and a stiff response in the Poisson rate are crucial to the transitional phenomena.

A fundamental question in the field of molecular computation is what computational tasks a biochemical system can carry out. In this work, we focus on the problem of finding the maximum likelihood estimate (MLE) for log-affine models. We revisit a construction due to Gopalkrishnan of a mass-action system with the MLE as its unique positive steady state, which is based on choosing a basis for the kernel of the design matrix of the model. We extend this construction to allow for any finite spanning set of the kernel, and explore how the choice of spanning set influences the dynamics of the resulting network, including the existence of boundary steady states, the deficiency of the network, and the rate of convergence. In particular, we prove that using a Markov basis as the spanning set guarantees global stability of the MLE steady state.

We study how environmental stochasticity influences the long-term population size in certain one- and two-species models. The difficulty is that even when one can prove that there is coexistence, it is usually impossible to say anything about the invariant probability measure which describes the coexisting species. We are able to circumvent this problem for some important ecological models by noticing that the per-capita growth rates at stationarity are zero, something which can sometimes yield information about the invariant probability measure. For more complicated models we use a recent result by Cuello to explore how small noise influences the population size. We are able to show that environmental fluctuations can decrease, increase, or leave unchanged the expected population size. The results change according to the dynamical model and, within a fixed model, also according to which parameters (growth rate, carrying capacity, etc) are affected by environmental fluctuations. Moreover, we show that not only do things change if we introduce noise differently in a model, but it also matters what one takes as the deterministic 'no-noise' baseline for comparison.

Human movement plays a key role in spreading vector-borne diseases globally. Various spatial models of vector-borne diseases have been proposed and analyzed, mainly focusing on disease dynamics. In this paper, based on a multi-patch Ross-Macdonald model, we study the impact of host migration on the local and global host disease prevalences. Specifically, we find that the local disease prevalence of any patch is bounded by the minimum and maximum disease prevalences of all disconnected patches and establish a weak order-preserving property. For global disease prevalence, we derive its formula at both zero and infinite dispersal rates and compare them under certain conditions, and calculate the right derivative at no dispersal. In the case of two patches, we give two complete classifications of the model parameter space: one is to compare the host disease prevalences with and without host dispersal, and the other is to determine the monotonicity of host disease prevalence with respect to host dispersal rate. Numerical simulations confirm inconsistence between disease persistence and host disease prevalence, as well as between host prevalence and vector prevalence in response to host movement. In general, a more uneven distribution of hosts and vectors in a homogeneous environment leads to lower host prevalence but higher vector prevalence and stronger disease persistence.

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.