Journal of Mathematical Biology最新文献

We examine a generalized KPP equation with a "q-diffusion", which is a framework that unifies various standard linear diffusion regimes: Fickian diffusion ( $q=0$ ), Stratonovich diffusion ( $q=1/2$ ), Fokker-Planck diffusion ( $q=1$ ), and nonstandard diffusion regimes for general $q\in R$ . Using both analytical methods and numerical simulations, we explore how the ability of persistence (measured by some principal eigenvalue) and how the asymptotic spreading speed depend on the parameter q and on the phase shift between the growth rate r(x) and the diffusion coefficient D(x). Our results demonstrate that persistence and spreading properties generally depend on q: for example, appropriate configurations of r(x) and D(x) can be constructed such that q-diffusion either enhances or diminishes the ability of persistence and the spreading speed with respect to the traditional Fickian diffusion. We show that the spatial arrangement of r(x) with respect to D(x) has markedly different effects depending on whether $q>0$ , $q=0$ , or $q<0$ . The case where r is constant is an exception: persistence becomes independent of q, while the spreading speed displays a symmetry around $q=1/2$ . This work underscores the importance of carefully selecting diffusion models in ecological and epidemiological contexts, highlighting their potential implications for persistence, spreading, and control strategies.

Pierre Magal (1967-2024) was a leading researcher at the interface of differential equations, functional analysis, and mathematical biology. He made substantial contributions to both theoretical and applied aspects of these subjects. He published a dozen monographs, proceedings, and special issues and more than 125 journal articles. In this article we provide an introduction to Pierre's contributions in some topics, including discrete population dynamics, integrated semigroup theory and abstract Cauchy problems with nondense domain, traveling waves in biological systems, uniform persistence and global attractors, cell-to-cell P-glycoprotein transfer in breast cancers, transfer problems in population dynamics and economics, and modeling of various epidemic problems, in particular his recent and extensive work on modeling COVID-19.

Go-or-grow approaches represent a specific class of mathematical models used to describe populations where individuals either migrate or reproduce, but not both simultaneously. These models have a wide range of applications in biology and medicine, chiefly among those the modeling of brain cancer spread. The analysis of go-or-grow models has inspired new mathematics, and it is the purpose of this review to highlight interesting and challenging mathematical properties of reaction-diffusion models of the go-or-grow type. We provide a detailed review of biological and medical applications before focusing on key results concerning solution existence and uniqueness, pattern formation, critical domain size problems, and traveling waves. We present new results related to the critical domain size and traveling wave problems, and we connect these findings to the existing literature. Moreover, we demonstrate the high level of instability inherent in go-or-grow models. We argue that there is currently no accurate numerical solver for these models, and emphasize that special care must be taken when dealing with the "monster on a leash".

We study the long time behaviour of a non-local parabolic integro-differential equation modelling the evolutionary dynamics of a phenotypically-structured population in a changing environment. Such models can arise in variety of contexts from climate change to chemotherapy to the ageing body. The main novelty is that there are two locally optimal traits, each of which shifts at a possibly different linear velocity. We determine sufficient conditions to guarantee extinction or persistence of the population in terms of associated eigenvalue problems. When the population does not go extinct, we study the behaviour of long time solutions in the case of rare mutations: the long time solution concentrates as a sum of Dirac masses on a point set of "lagged optima" which are strictly behind the true shifting optima as the mutation rate goes to zero. If we further assume the shift velocities are different, we show the solution concentrates specifically on the positive lagged optimum with maximum lagged fitness. Our results imply that for populations undergoing competition in temporally changing environments, both the true optimal fitness and the required rate of adaptation for each of the diverging optimal traits determine the eventual dominance of one trait.

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.