Journal of Mathematical Biology最新文献

We consider a generalized version of the birth-death (BD) and death-birth (DB) processes introduced by Kaveh et al. (R Soc Open Sci 2(4):140465. https://doi.org/10.1098/rsos.140465 ), in which two constant fitnesses, one for birth and the other for death, describe the selection mechanism of the population. Rather than constant fitnesses, in this paper we consider more general frequency-dependent fitness functions (allowing any smooth functions) under the weak-selection regime. A particular case arises in evolutionary games on graphs, where the fitness functions are linear combinations of the frequencies of types. For a large population structured as a star graph, we provide approximations for the fixation probability which are solutions of certain ODEs (or systems of ODEs). For the DB case, we prove that our approximation has an error of order 1/N, where N is the size of the population. The general BD and DB processes contain, as special cases, the BD-* and DB-* (where * can be either B or D) processes described in Hadjichrysanthou et al. (Dyn Games Appl 1(3):386. https://doi.org/10.1007/s13235-011-0022-7 )-this class includes many examples of update rules used in the literature. Our analysis shows how the star graph may act as an amplifier, suppressor, or remains isothermal depending on the scaling of the initial mutant placement. We identify an analytical threshold for this transition and illustrate it through applications to evolutionary games, which further highlight asymmetric structural effects across different game types. Numerical examples show that our fixation probability approximations remain accurate even for moderate population sizes and across a wide range of frequency-dependent fitness functions, extending well beyond previously studied linear cases derived from evolutionary games, or constant fitness scenarios.

The evolution of certain phenotypic traits can be influenced both by natural pressures, such as asymmetric competition, and by anthropogenic pressures, such as the severe and prolonged emission of pollutants generated by human activity. In this study, we propose a new nonlinear and non-autonomous mathematical model to analyze the adaptive dynamics of a continuous phenotypic trait in a single-species population, simultaneously exposed to asymmetric competition and to chronic and critical pollution. The model considers both exogenous sources, such as chemical or acoustic emissions, and endogenous sources derived from compensatory mechanisms, such as metabolic detoxification or the Lombard effect. We employ methods from population and adaptive dynamics, complemented by numerical simulations, to determine the conditions under which a convergently stable evolutionary strategy can remain continuously stable or become an evolutionary branching point that promotes phenotypic diversification. The results show that asymmetric competition drives evolution toward higher trait values, although increasing costs may induce evolutionary branching. In contrast, pollution tends to limit such evolution, favoring its stabilization at lower values. The interaction between both pressures can give rise to different adaptive trajectories depending on how evolutionary costs vary. Finally, we apply our theoretical results to a case of acoustic pollution in species that experience the Lombard effect. This model is presented as a useful tool for anticipating evolutionary trajectories in polluted environments and for supporting adaptive conservation strategies in the face of global change.

Turing patterns in reaction-diffusion (RD) systems have traditionally been studied only in systems that do not explicitly depend on independent variables such as space. In practice, many systems in which Turing patterning is important are not homogeneous and do not possess ideal boundary conditions. In heterogeneous systems with stable steady states, the steady states themselves are also necessarily heterogeneous, which is problematic for analytical approaches. Whilst there has been a large body of work extending Turing analysis to certain heterogeneous systems, it remains difficult-especially on small domains-to determine whether a stable patterned state arises purely from system heterogeneity or whether a Turing instability plays a role. This also complicates numerical investigations into critical domain lengths for such instabilities. In this work, we propose a framework that uses numerical continuation to map heterogeneous RD systems onto a nearby homogeneous system. This framework may be used to analyse the role of Turing instabilities in generating patterns in heterogeneous RD systems. We study the Schnakenberg and Gierer-Meinhardt models with spatially heterogeneous production as test problems. Our investigation reveals the following features. For sufficiently large system heterogeneity (i.e., large-amplitude spatial variations in morphogen production), it is possible for Turing-patterned and base states to become coincident and therefore indistinguishable. This only occurs when a Turing instability is present in a nearby homogeneous reaction-diffusion system. In fact, an instability must occur in a mode that is at least resonant with, or of higher frequency than, the spatial frequency of the system heterogeneity, implying that a resonance effect governs the breakdown of the base state definition. Otherwise, a base state-by our definition-can always be found. Furthermore, we provide numerical evidence that, in the case of large domains, the homotopy-based base state definition we propose agrees with that found in the literature. We then use this base state definition to numerically investigate critical domain lengths in systems with spatial heterogeneity, which give rise to regions that locally support Turing patterning.

For two resource-sharing species we explore the interplay of harvesting and dispersal strategies, as well as their influence on competition outcomes. Although the extinction of either species can be achieved by excessive culling, choosing a harvesting strategy such that the biodiversity of the populations is preserved is much more complicated. We propose a type of heterogeneous harvesting policy, dependent on dispersal strategy, where the two managed populations become an ideal free pair, and show that this strategy guarantees the coexistence of the species. We also show that if the harvesting of one of the populations is perturbed in some way, then it is possible for the coexistence to be preserved. Further, we show that if the dispersal of two species formed an ideal free pair, then a slight change in the dispersal strategy for one of them does not affect their ability to coexist. Finally, in the model, directed movement is represented by the term $\Delta (u/P)$ , where P is the dispersal strategy and target distribution. We justify that once an invading species, which has an advantage in carrying capacity, chooses a dispersal strategy that mimics the resident species distribution, then successful invasion is guaranteed. However, numerical simulations show that invasion may be successful even without an advantage in carrying capacity. More work is needed to understand the conditions, in addition to targeted culling, under which the host species would be able to persist through an invasion.

In this paper, spreading properties of reaction-diffusion systems with cooperative and reducible nonlinearity are considered. Weinberger et al. [J. Math. Biol. 45 (2002) 183-218] demonstrated that components of reducible cooperative systems can spread at distinct finite speeds for given compactly supported initial conditions. We extend this analysis by considering the possible acceleration spreading. Our findings reveal that all components can propagate at different speeds, either linearly or superlinearly (acceleration). By employing the graph theory, we specifically characterize the level sets of solutions, illustrating the influence of the cooperative effect. Examples are presented to illustrate the obtained results.

Cholera is an acute diarrheal disease caused by the bacterium Vibrio cholerae. With the consideration of the transmission mechanism and heterogeneity of population, an age-structured cholera epidemic model is proposed, involving saturation incidence rates that describe direct and indirect transmission pathways and all class-ages with the susceptible age of susceptible individuals, infection age of infected individuals and biological age of Vibrio cholerae. The focus is to investigate the global dynamics of the model by using the basic reproduction number $R_0$ . After establishing the well-posedness of the initial-boundary value problem of the model, we study the existence of endemic steady state and local stability of the disease-free steady state in terms of $R_0$ . Next asymptotic smoothness of the semi-flow is discussed in order to obtain the existence of a global attractor. Finally, global stability of the disease-free and endemic steady states is obtained by combining Volterra-type Lyapunov functionals and existence of global attractors. Numerical simulations are given to demonstrate the effect of age structures and to illustrate the theoretical results.

Agent-based modeling (ABM) is a powerful computational approach for studying complex biological and biomedical systems, yet its widespread use remains limited by significant computational demands. As models become increasingly sophisticated, the number of parameters and interactions rises rapidly, exacerbating the so-called "curse of dimensionality" and making comprehensive parameter exploration and uncertainty analyses computationally prohibitive. A growing body of work points to surrogate modeling as a powerful approach for approximating the dynamics of agent-based models, providing computationally efficient pathways for tasks such as parameter estimation, sensitivity analysis, and uncertainty quantification. In this review, we examine traditional approaches for performing these tasks directly within ABMs-providing a baseline for comparison-and then synthesize recent developments in surrogate-assisted methodologies for biological and biomedical applications. We cover statistical, mechanistic, and machine-learning-based approaches, emphasizing emerging hybrid strategies that integrate mechanistic insights with machine learning to balance interpretability and scalability. Finally, we discuss current challenges and outline directions for future research, including the development of standardized benchmarks to enhance methodological rigor and facilitate the broad adoption of surrogate-assisted ABMs in biology and medicine.

The key to a robust life system is to ensure that each cell population is maintained in an appropriate state. In this work, a mathematical model is used to investigate the control of the switching between the migrating and non-migrating states of the Bacillus subtilis cell population. In this case, the motile cells and matrix producers are the predominant cell types in the migrating cell population and non-migrating state, respectively, and can be suitably controlled according to the environmental conditions and cell density information. A minimal smooth model consisting of four ordinary differential equations is used as the mathematical model to control the B. subtilis cell types. Furthermore, the necessary and sufficient conditions for the hysteresis, which pertains to the change in the pheromone concentration, are clarified. In general, the hysteretic control of the cell state enables stable switching between the migrating and growth states of the B. subtilis cell population, thereby facilitating the biofilm life cycle. The results of corresponding culture experiments are examined, and the obtained corollaries are used to develop a model to input environmental conditions, especially, the external pH. On this basis, the environmental conditions are incorporated in a simulation model for the cell type control. In combination with a mathematical model of the cell population dynamics, a prediction model for colony growth involving multiple cell states, including concentric circular colonies of B. subtilis, can be established.

Cerebral blood flow regulation is critical for brain function, and its disruption is implicated in various neurological disorders. Many existing models do not fully capture the complex, multiscale interactions among neuronal activity, astrocytic signaling, and vascular dynamics, especially in key brainstem regions. In this work, we present a 3D-1D-0D multiscale computational framework for modeling the neuro-glial-vascular unit (NGVU) in the dorsal vagal complex (DVC). Our approach integrates a quadripartite synapse model, which captures the dynamic interactions among excitatory and inhibitory neurons, astrocytes, and vascular smooth muscle cells, with a hierarchical description of vascular dynamics that couples a three-dimensional microcirculatory network with a one-dimensional macrocirculatory representation and a zero-dimensional synaptic component. By linking neuronal spiking, astrocytic calcium and gliotransmitter signaling, and vascular tone regulation, our model reproduces key features of neurovascular regulation and elucidates the feedback loops that help maintain cerebral blood flow. Simulation results demonstrate that neurotransmitter release triggers astrocytic responses that modulate vessel radius, thereby influencing local oxygen and nutrient delivery. This integrated framework provides a robust and modular platform for future investigations into the pathophysiology of cerebral blood flow regulation and its role in autonomic control, including the regulation of gastric function.

Stochastic epidemic modeling has become increasingly crucial for assessing the severity of infectious diseases, attracting considerable attention in recent years. In this paper, we present three Markov-based epidemic models that incorporate demographic dynamics, including births, deaths, and migration. The inclusion of transition rates associated with these factors defines open-population systems, leading to a time-dependent transition pattern from the susceptible to the infectious phase. Notably, this work is the first to investigate epidemic models with time-varying population sizes within a Markovian framework. Furthermore, we introduce novel computational approaches for estimating stochastic features related to the number of secondary infections originating from an index case and the onset of a hazard (hitting) time associated with the number of susceptible cases in the system. Through extensive sensitivity analysis, we assess the impact of demographic dynamics on these descriptors and, consequently, on the severity of epidemic outbreaks. To validate the effectiveness of the introduced models, we utilize data from the 2022 mpox outbreak in Greece and examine the effect of interventions such as lockdowns on disease severity. This analysis helps health authorities identify optimal initiation periods and more effectively adjust the stringency of restrictive measures.