Journal of Mathematical Biology最新文献

The linear noise approximation (LNA) describes the random fluctuations from the mean-field concentrations of a chemical reaction network due to intrinsic noise. It is also used as a test probe to determine the accuracy of reduced formulations of the chemical master equation and to understand the relationship between timescale disparity and model reduction in stochastic environments. Although several reduced LNAs have been proposed, they have not been placed into a general theory concerning the accuracy of reduced LNAs derived from center manifold and singular perturbation theory. This has made it difficult to understand why certain reductions of the master or Langevin equations fail or succeed. In this work, we develop a deeper understanding of slow manifold projection in the linear noise regime by answering a straightforward but open question: In the presence of eigenvalue disparity, does the appropriate oblique projection of the LNA onto the slow eigenspace accurately approximate the first and second moments of complete LNA, and if not, why? Although most studies concentrate on the role of eigenvalue disparity arising from the drift matrix, we go further and examine the interplay between disparate 'drift" eigenvalues and the eigenvalues of the diffusion matrix, the latter of which may or may not be disparate. Furthermore, we place the previously established reductions of the LNA into a more general framework and formulate the necessary and sufficient conditions for the projected LNA to accurately approximate the first and second moments of the complete LNA.

Crohn's disease (CD) is a recurrent chronic autoimmune disease, which is an inflammatory disease of the intestine with epithelial granulomas. The number of patients has been increasing significantly, and its pathogenesis and treatments are arousing hot discussions in the academic community. Taking into account the spatial heterogeneity of lesion distribution and the periodic recurrence, this paper uses a partial functional differential system with the free diffusion of bacteria and immunocytes and immune response latency to model the process of CD, based on the Lauffenburger-Kennedy bacterial infection model. In order to describe the spatial distribution and recurrence, we analyze the stability of the inflammation equilibrium state, and deduce the diffusion-driven Turing bifurcations and delay-driven Hopf bifurcations, drive the critical conditions for occurrence. Furthermore, through the analysis of Turing-Hopf bifurcations, the coupling effect of two factors is explored to obtain spatiotemporal patterns that better reflect clinical manifestations of CD. In addition, both theoretical and numerical results reveal that the motility is a necessary factor in the production of intestinal epithelial granulomas, while the immune response latency is an important factor in the recurrence. A small effective diffusion rate and a large time delay would lead to two spatially non-homogeneous steady states and a stable periodic solution, ultimately giving rise to a pair of stable spatially non-homogeneous periodic solutions through Turing-Hopf bifurcations. Our conclusions may provide some insights into the control mechanisms for Crohn's disease.

Cardiovascular disease continues to be the leading cause of death in the United States. A major contributing factor is cardiac arrhythmia, which results from irregular electrical activity in the heart. On a tissue level, cardiac conduction involves the spread of action potentials (AP) across the heart, enabling coordinated contraction of the myocardium. On a cellular level, the transmission of signals between cells is facilitated by low-resistance pathways formed by gap junctions (GJs). Recent experimental studies have sparked discussion on whether GJs play a dominant role in cell communication. Interestingly, research has revealed that GJ knockout mice can still demonstrate signal propagation in the heart, albeit more slowly and discontinuously, indicating the presence of an alternative mechanism for cardiac conduction. Unlike GJ-mediated propagation, ephaptic coupling (EpC) has emerged as a distinct form of electrical transmission, characterized by contactless electrochemical signaling across the narrow intercalated discs (IDs) between cardiomyocytes. Advancements in cardiac research have highlighted the crucial role of EpC in restoring conduction by increasing conduction velocity (CV), reducing conduction block (CB), and terminating reentry arrhythmias, particularly when GJs are impaired. However, most EpC studies are either numerical or experimental, while analytical studies on ephaptic conduction-an equally important aspect of understanding EpC-remain extremely limited. In this paper, we applied asymptotic theory to calculate the CV in the presence of weak EpC. To achieve this, we developed both continuous and discrete models to describe ephaptic conduction along a strand of cells. Ionic dynamics were modeled using the piecewise linear and cubic functions. The resulting system represents a bistable system with weak EpC. We calculated an expression for CV in the presence of weak EpC for both models, and validated our analytical results with numerical simulations. Additionally, we showed that under weak EpC, CV can increase if the distribution of INa is more prominent on the end membrane.

The identification of psychosocial risk and protective factors associated with substance use during adolescence is crucial for the prevention and treatment of addictive behaviors. However, in the mathematical modeling of addictions, these psychological and social dimensions are often addressed in isolation. By focusing on the immediate socialization environment of adolescents, comprising peers, parents and family, and school, and considering them as risk and protective factors, we mathematically model binge drinking behavior from interaction dynamics among individuals and their predisposition to consumption based on evolutionary and adaptive reasons. Our findings indicate that, in the face of negative peer influence, prosocial behaviors, as well as supportive attitudes from parents and family, and the school environment, have the potential to inhibit long-term binge drinking. This tendency is strengthened when protective situations are consistently promoted in response to risky scenarios, which is in line with both theoretical approaches to prevention and current public policy on drug consumption.

Zero-one biochemical reaction networks play key roles in cell signalling such as signalling pathways regulated by protein phosphorylation. Multistability of reaction networks is a crucial dynamics feature enabling decision-making in cells. It is well known that multistability can be lifted from a "subnetwork" (a network with less species and fewer reactions) to large networks. So, we aim to explore the multistability problem of small zero-one networks. In this work, we prove the following main results: 1. any zero-one network with a one-dimensional stoichiometric subspace admits at most one positive steady state (it must be stable), and all the one-dimensional zero-one networks can be classified according to if they indeed admit a stable positive steady state or not; 2. any two-dimensional zero-one network with up to three species either admits only degenerate positive steady states, or admits at most one positive steady state (it must be stable); 3. the smallest zero-one networks (here, by "smallest", we mean these networks contain species as few as possible) that admit nondegenerate multistationarity/multistability contain three species and five/six reactions, and they are three-dimensional. In these proofs, we use the theorems based on the Brouwer degree theory and the theory of real algebraic geometry. Moreover, applying the tools of computational real algebraic geometry, we provide a systematical way for detecting the networks that admit nondegenerate multistationarity/multistability.

The closed fishing season policy plays a crucial role in fishery management by contributing to the restoration and protection of fishery resources, maintaining ecological balance and promoting sustainable development. The population dynamics of fish, particularly marine species, are highly complex. Under the combined effects of ecological mechanisms (such as predation, resource limitations, and competition), fish populations can exhibit multiple stable states. Overfishing increases the vulnerability of fish populations, making them prone to shift from a high-density stable state to a low-density one, and in some cases, leading to the risk of extinction. In this context, developing effective closed fishing season policies to ensure the sustainable development of fishery resources has become a pressing issue. In this paper, we propose a reaction-diffusion model consisting of two sub-equations with multiple stable states and a linear harvesting rate to describe the continuous switching between closed and open fishing seasons. We define a threshold value $\overline{T}_{}^{\ast }$ for the duration of the fishing ban $\overline{T}$ . When $\overline{T}\le \overline{T}_{}^{\ast }$ , the trivial stable state is globally asymptotically stable. Uniqueness of periodic solutions is generally a mathematically challenging problem. However, employing the comparison theorem, we find that conditions on the uniqueness of periodic solutions to the associated ODE system are also applicable to our model. Specifically, under certain conditions, when $\overline{T}>\overline{T}_{}^{\ast }$ , we provide sufficient conditions on the existence of a globally asymptotically stable periodic solution. Finally, we offer discussion and numerical simulations to illustrate our findings.

We consider a model for the spread of an influenza-like disease in which, between seasons, the virus makes a random genetic drift (reducing immunity) and obtains a new random transmissibility (closely related to $R_0$ ). Given the immunity status at the start of season k, i.e. the community distribution of years since last infection and their associated immunity levels, the outcome of the epidemic season k, characterized by the effective reproduction number $R_e^{\left(k\right)}$ and the fractions infected in the different immunity groups $z^{\left(k\right)}$ , is determined by the random genetic drift and transmissibility. It is shown that the community immunity status of consecutive seasons, is an ergodic Markov chain, which converges to a stationary distribution. More analytical progress is made for the case where immunity only lasts for one season: we then characterize the stationary distribution of the community fraction having partial immunity (from being infected last season) as well as the stationary distribution of $(R_e^{\left(k\right)},z^{\left(k\right)})$ , and the conditional distribution of $z^{\left(k\right)}$ given $R_e^{\left(k\right)}$ . The effective reproduction number $R_e^{\left(k\right)}$ is closely related to the initial exponential growth rate ${\rho }^{\left(k\right)}$ of the outbreak, a quantity which can be estimated early in the epidemic season. As a consequence, this conditional distribution may be used for predicting the final size of the epidemic based on its initial growth and immunity status.

Competitive exclusion principle, which states that two or more species limited by the same resource cannot coexist indefinitely, is a very common phenomenon in population dynamics. It is well-known that competitive exclusion principle occurs in deterministic competition models, diffusive competition models, and evolutionary competition models. In this paper, we consider an age-structured competition model among N species and obtain an interesting result: under suitable scaled birth and death rates, the species with the smallest maximum age always wins the competition to exclude the other species; that is, the competitive exclusion principle occurs in age-structured competition models.

Continuous time Markov chains are commonly used as models for the stochastic behavior of chemical reaction networks. More precisely, these Stochastic Chemical Reaction Networks (SCRNs) are frequently used to gain a mechanistic understanding of how chemical reaction rate parameters impact the stochastic behavior of these systems. One property of interest is mean first passage times (MFPTs) between states. However, deriving explicit formulas for MFPTs can be highly complex. In order to address this problem, we first introduce the concept of [Formula: see text] and develop theorems to determine whether certain SCRNs have this feature by studying associated graphs. Additionally, we develop an algorithm to identify, under specific assumptions, all possible coclique level structures associated with a given SCRN. Finally, we demonstrate how the presence of such a structure in a SCRN allows us to derive closed form formulas for both upper and lower bounds for the MFPTs. Our methods can be applied to SCRNs taking values in a generic finite state space and can also be applied to models with non-mass-action kinetics. We illustrate our results with examples from the biological areas of epigenetics, neurobiology and ecology.