Journal of Mathematical Biology最新文献

In Lou et al. (Lou Y, Tao W, Wang Z-A. Effects and biological consequences of the predator-mediated apparent competition I: ODE models. J. Math. Biol. 91 (2025), 47, 37 pages), the authors investigated the effects and biological consequences of the predator-mediated apparent competition using a temporal (ODE) system consisting of one predator and two prey species (one is native and the other is invasive) with Holling type I and II functional responses. This paper is a sequel to Lou et al. (Lou Y, Tao W, Wang Z-A. Effects and biological consequences of the predator-mediated apparent competition I: ODE models. J. Math. Biol. 91 (2025), 47, 37 pages.), by including spatial movements (diffusion and prey-taxis) into the ODE system and examining the spatial effects on the population dynamics under the predator-mediated apparent competition. We establish the global boundedness of solutions in a two-dimensional bounded domain with Neumann boundary conditions and the global stability of constant steady states in certain parameter regimes, by which we find a threshold dynamics in terms of the predator's death rate. For the parameters outside the global stability regimes, we conduct a linear stability analysis to show that diffusion and/or prey-taxis can induce instability by both steady-state and Hopf bifurcations. We further use numerical simulations to illustrate that various spatial patterns are all possible, including stable spatial aggregation patterns, spatially homogeneous but time-periodic patterns, and spatially inhomogeneous and time-oscillatory patterns. It comes with a surprise that either of diffusion and prey-taxis can induce steady-state or Hopf bifurcations to generate intricate spatial patterns in the one predator-two prey system, which is sharply different from the one predator-one prey system for which neither diffusion nor prey-taxis can induce spatial patterns. These results show that spatial movements play profound roles in the emerging properties for predator-prey systems with multiple prey species. We also find that prey-taxis may play dual roles (stabilization and destabilization) and facilitate the predator-mediated apparent competition to eliminate the native prey species under the moderate initial mass of invasive prey species.

HIV infection, a leading cause of AIDS, continues to impose a substantial global health burden. This study investigates the mechanisms of HIV infection and immune responses through a delayed infection-age structured model that integrates viral target cell infection, CTLs-mediated immunity, and delayed antibody immune responses. We rigorously analyze the existence, uniqueness, and boundedness of the model's solution semi-flow, followed by detailed examinations of equilibrium states coexistence and local stability. Using clinical HIV case data from Jiangsu Province, we estimate model parameters and assess fitting accuracy. The model successfully replicates key clinical manifestations in four ART-treated patients, underscoring its medical relevance. Our findings suggest that ART efficacy primarily manifests in reduced infection rates and viral release rates. Notably, reverse transcriptase inhibitors, fusion inhibitors, and entry inhibitors demonstrate significantly superior therapeutic efficacy compared to protease inhibitors and treatments targeting drug-resistant viral strains. Moreover, ART exhibits significantly stronger enhancement of cellular immunity (particularly CD8+ T cell responses) than modulation of humoral immunity, viral reservoirs persist despite potent antiretroviral suppression.

Mathematical modeling is essential for understanding infectious disease dynamics and guiding public health strategies. We study the global dynamics of a susceptible-infectious-recovered-susceptible (SIRS) model with a generalized nonlinear incidence function, revealing a rich array of bifurcation phenomena, including saddle-node, cusp, forward and backward bifurcations, Bogdanov-Takens bifurcations, saddle-node bifurcation of limit cycles, subcritical and supercritical Hopf bifurcations, generalized Hopf bifurcations, homoclinic and degenerate homoclinic bifurcations, as well as isola bifurcation. Using normal form theory, we show that the Hopf bifurcation reaches codimension three, resulting in up to three small-amplitude limit cycles. The involvement of the recovered population enables coexistence of these limit cycles, leading to bistable and tristable dynamics. We employ a one-step transformation method to analyze codimension two and three Bogdanov-Takens bifurcations, confirming a maximum codimension of three. In particular, we identify isolas of limit cycles in an SIRS model involving double exposure, introducing a mechanism for generating limit cycles centered on the isola. The findings may have important public health implications, highlighting how nonlinearities in transmission and immunity can produce recurrent outbreaks or persistent infection despite interventions. The existence of multiple limit cycles suggests that small changes in transmission rates or immune response could cause abrupt shifts in outbreak patterns, emphasizing the need for adaptive and flexible intervention strategies.

The year 2024 marked the 50th anniversary of the Journal of Mathematical Biology. The journal was founded in 1974 with the vision to build a platform for advanced mathematical methods as they are applied and developed for biological problems. What began as a small journal for a specialized group of experts has grown into a flag-ship journal of a large and ever expanding field. We celebrate this occasion with a Special Collection of papers from our Associate Editors and our past and present Editors in Chief to showcase the state of the art and stimulate interesting new research directions in Mathematical Biology.

The mussel-algae (M-A) system plays a crucial role in maintaining the balance of marine aquaculture ecosystems. Mussels filter algae from the water as a food source, while algae produce oxygen through photosynthesis and contribute to nutrient cycling. Fluctuations in the density and spatial distribution of algae populations can significantly impact the growth and reproduction of mussels, and conversely, mussels can influence algae dynamics, thereby potentially altering the equilibrium of the system. This study adopts a practical perspective, simultaneously considering the effects of self-diffusion and cross-diffusion, and establishes a spatiotemporally discretised coupled map lattices (CMLs) model for the M-A system. Utilising linear stability analysis, bifurcation theory, and the centre manifold theorem, we explore the stability and classification of fixed points within the CMLs model, as well as the parameter conditions that give rise to flip and Turing bifurcations. Numerical simulations demonstrate the rich temporal dynamics and spatiotemporal patterns induced by five different mechanisms. Notably, we introduce a proportional-differential (PD) control into the CMLs model for the first time. Through numerical simulations, we validate that the PD control can delay the occurrence of the flip bifurcation, thereby preventing multi-period oscillations and chaos in algal population density, which could lead to system instability. Moreover, the PD control can reduce the Turing instability region and adjust the Turing pattern types induced by the five mechanisms, thus ensuring a uniform spatiotemporal distribution of the algal population and contributing to the stability of the ecosystem.

Non-adherence to prescribed medications, typically manifested as random dosing times and variable dosages, is a significant obstacle in disease treatment. Existing model-based studies often rely on assumptions as dose omissions or random dosing times, which fails to represent the multifaceted nature of non-adherence. In this study, we propose a one-compartment stochastic pharmacokinetic model incorporating dual-randomness in dosing times and dosages. Our objective is to analyze how dual-randomness affects drug concentration variability, and to develop dosage adjustment strategies for the desired concentration. Leveraging the renewal process, the law of total expectation, and the theory of second-type Volterra integral equations, the statistical properties of drug concentrations under general distributions in dosing times and dosages are derived, including characteristic function, expectation, variance, and so on. Given specific uniform and exponential distributions of inter-dose time intervals, the explicit expressions of statistical characteristics are obtained, and the dosage adjustment strategies to acquire the desired concentration are theoretically proposed. Our findings establish a theoretical foundation for understanding drug concentration variability within a dual-randomness framework, thereby providing critical insights for risk prevention and process control in drug therapy during disease treatment.

Natural populations experience a complex interplay of continuous and discrete processes: continuous growth and interactions are punctuated by discrete reproduction events, dispersal, and external disturbances. These dynamics can be modeled by impulsive or flow-kick systems, where continuous flows alternate with instantaneous discrete changes. To study species persistence in these systems, an invasion growth rate theory is developed for flow-kick models with state-dependent timing of kicks and auxiliary variables that can represent stage structure, trait evolution, or environmental forcing. The invasion growth rates correspond to Lyapunov exponents that characterize the average per-capita growth of species when rare. Two theorems are proven that use invasion growth rates to characterize permanence, a form of robust coexistence where populations remain bounded away from extinction. The first theorem uses Morse decompositions of the extinction set and requires that there exists a species with a positive invasion growth rate for every invariant measure supported on a component of the Morse decomposition. The second theorem uses invasion growth rates to define invasion graphs whose vertices correspond to communities and directed edges to potential invasions. Provided the invasion graph is acyclic, permanence and extinction are fully characterized by the signs of the invasion growth rates. Invasion growth rates are also used to identify the existence of extinction-bound trajectories and attractors that lie on the extinction set. To demonstrate the framework's utility, these results are applied to three ecological systems: (i) a microbial serial transfer model where state-dependent timing enables coexistence through a storage effect, (ii) a spatially structured consumer-resource model showing intermediate reproductive delays can maximize persistence, and (iii) an empirically parameterized Lotka-Volterra model demonstrating how disturbance can lead to extinction by disrupting facilitation. Mathematical challenges, particularly for systems with cyclic invasion graphs, and promising biological applications are discussed. These results reveal how the interplay between continuous and discrete dynamics creates ecological outcomes not found in purely continuous or discrete systems, providing a foundation for predicting population persistence and species coexistence in natural communities subject to gradual and sudden changes.

We present a model of infectious disease dynamics where individuals can transition between different compartments, which may have distinct epidemiological characteristics. Within each compartment, epidemic dynamics are represented by a staged progression epidemic model. Individual transitions between compartments occur on a faster time scale, allowing the initial model to be reduced for analysis. In the reduced model, disease eradication and endemicity are characterized by the basic reproduction number. The relationship between this basic reproduction number and those associated with each compartment is analyzed by considering each compartment in isolation. This allows the study of the role of transitions in epidemic dynamics. Endemicity is represented by uniform persistence relative to the total number of infected individuals. It is verified that, for a sufficiently large ratio between time scales, the initial model shares the uniform persistence of the reduced model. The influence of transitions on disease eradication/endemicity is illustrated by different results. In particular, the conditions for transition rates are determined so that endemicity (eradication) in each isolated compartment results in global eradication (endemicity). These results can provide some tools for managing epidemics in the context of individuals transiting between compartments with different epidemiological properties.

An adult human body is made up of some 30 to 40 trillion cells, all of which stem from a single fertilized egg cell. The process by which the right cells appear to arrive in their right numbers at the right time at the right place - development - is only understood in the roughest of outlines. This process does not happen in isolation: the egg, the embryo, the developing foetus, and the adult organism all interact intricately with their changing environments. Conceptual and, increasingly, mathematical approaches to modelling development have centred around Waddington's concept of an epigenetic landscape. This perspective enables us to talk about the molecular and cellular factors that contribute to cells reaching their terminally differentiated state: their fate. The landscape metaphor is however only a simplification of the complex process of development; it for instance does not consider environmental influences, a context which we argue needs to be explicitly taken into account and from the outset. When delving into the literature, it also quickly becomes clear that there is a lack of consistency and agreement on even fundamental concepts; for example, the precise meaning of what we refer to when talking about a 'cell type' or 'cell state.' Here we engage with previous theoretical and mathematical approaches to modelling cell fate - focused on trees, networks, and landscape descriptions - and argue that they require a level of simplification that can be problematic. We introduce random dynamical systems as one natural alternative. These provide a flexible conceptual and mathematical framework that is free of extraneous assumptions. We develop some of the basic concepts and discuss them in relation to now 'classical' depictions of cell fate dynamics, in particular Waddington's landscape. This paper belongs to the special issue "Problems, Progress and Perspectives in Mathematical and Computational Biology".

Predator-mediated apparent competition is an indirect negative interaction between two prey species mediated by a shared predator, which can lead to changes in population dynamics, competition outcomes and community structures. This paper is devoted to investigating the effects and biological consequences of the predator-mediated apparent competition based on a two prey species (one is native and the other is invasive) and one predator model with Holling type I and II functional responses. Through the analytical results and case studies alongside numerical simulations, we find that the initial mass of the invasive prey species, capture rates of prey species, and the predator mortality rate are all important factors determining the success/failure of invasions and the species coexistence/extinction. The global dynamics can be completely classified for the Holling type I functional response, but can only be partially determined for the Holling type II functional response. For the Holling type I functional response, we find that whether the invasive prey species can successfully invade to induce the predator-mediated apparent competition is entirely determined by the capture rates of prey species. For the Holling type II functional response, the dynamics are more complicated. First, if two prey species have the same ecological characteristics, then the initial mass of the invasive prey species is the key factor determining the success/failure of the invasion and hence the effect of the predator-mediated apparent competition. Whereas if two prey species have different ecological characteristics, say different capture rates, then the success of the invasion no longer depends on the initial mass of the invasive prey species, but on the capture rates. In all cases, if the invasion succeeds, then the predator-mediated apparent competition's effectiveness essentially depends on the predator mortality rate. Precisely we show that the native prey species will die out (resp. persist) if the predator has a low (resp. moderate) mortality rate, while the predator will go extinct if it has a large mortality rate. Our study reveals that predator-mediated apparent competition is a complicated ecological process, and its effects and biological consequences depend upon many possible factors.