Journal of Mathematical Biology最新文献

In areas infested with Aedes aegypti mosquitoes it may be possible to control dengue, and some other vector-borne diseases, by introducing Wolbachia-infected mosquitoes into the wildtype population. Thus far, empirical and theoretical studies of Wolbachia release have tended to focus on the dynamics at the community scale. However, Ae. aegypti mosquitoes typically dwell in and around the same houses as the people they bite and it can be insightful to explore what happens at the household scale where small population sizes lead to inherently stochastic dynamics. Here we use a continuous-time Markov framework to develop a stochastic household model for small populations of wildtype and Wolbachia-infected mosquitoes. We investigate the transient and long term dynamics of the system, in particular examining the impact of stochasticity on the Wolbachia invasion threshold and bistability between the wildtype-only and Wolbachia-only steady states previously observed in deterministic models. We focus on the influence of key parameters which determine the fitness cost of Wolbachia infection and the probability of Wolbachia vertical transmission. Using Markov and matrix population theory, we derive salient characteristics of the system including the probability of successful Wolbachia invasion, the expected time until invasion and the probability that a Wolbachia-infected population reverts to a wildtype population. These attributes can inform strategies for the release of Wolbachia-infected mosquitoes. In addition, we find that releasing the minimum number of Wolbachia-infected mosquitoes required to displace a resident wildtype population according to the deterministic model, only results in that outcome about 20% of the time in the stochastic model; a significantly larger release is required to reach a steady state composed entirely of Wolbachia-infected mosquitoes 90% of the time.

In order to investigate the spatial distribution and evolution dynamics of populations exhibiting synchronized reproduction and two stage long-distance dispersal modes, in this paper we propose an impulsive integro-differential model with non-local pulse. Firstly, we establish the extinction and persistence dynamics on the bounded domain with Dirichlet boundary of non-local type. Secondly, we derive the existence and characterization of the spreading speed in the whole space as well as the consistency with the minimum wave speed of the traveling waves. Finally, numerical simulations are presented to study the effects of different dispersal patterns and dispersal allocation strategy on population persistence and spreading speed under a constant measure of total dispersal. Our results show that under the same overall variance, the non-local diffusion pattern has both higher steady-state density and greater spreading speed than the local diffusion pattern. Moreover, under the fixed total dispersal, the optimal state for both population persistence and spreading speed is usually achieved through a stage-concentrated dispersal strategy, where dispersal occurs in a single life stage and the other stages remain sedentary. Additionally, we numerically investigate the impact of overcompensation on threshold and propagation dynamics, serving as a complement to the theoretical results in the non-monotonic case. This work provides new insights into the understanding of non-local interactions in biology and ecology.

Both virus-to-cell and cell-to-cell transmission modes play a crucial role in the long-term dynamics of HIV infection. Additionally, the immune response - particularly the activity of cytotoxic T lymphocytes (CTLs) - can significantly influence the threshold conditions for viral persistence. By incorporating age-structured within-host virus dynamics and the immune response, we develop a dynamical model to explore the intricacies of HIV transmission and progression within a detailed mathematical framework. Specifically, by analyzing the characteristic equations, we establish the local stability of the feasible steady states. Using Lyapunov functionals and LaSalle's invariance principle, we demonstrate that the global threshold dynamics of the model can be described by the immune-inactivated and immune-activated reproduction rates. This study provides a more accurate representation of the complex interplay between HIV and the immune system, offering valuable insights for potential therapeutic strategies.

In biological systems, cooperative behavior forms the foundation for the survival and prosperity of many organisms. However, the finite nature of resources often drives selfish individuals to exploit resources through deceptive tactics, thereby instigating conflicts between collective and individual interests. These strategic interactions not only alter the availability of environmental resources but also feedback on the strategic choices of populations, leading to the co-evolution of environmental resources and behavioral strategies. By integrating population dynamics with replicator dynamics, we develop models for both well-mixed and spatially heterogeneous distributions that incorporate resource feedback mechanisms to analyze the intricate interplay between cooperative behavior and resource dynamics across temporal and spatial scales. Our findings reveal complex evolutionary dynamics, including rich multistability, transcritical and Hopf bifurcations in the temporal system, alongside spatial stability, Turing instability, Turing-Hopf bifurcation, and chaotic behavior in the spatial diffusion system. In homogeneous distributions, payoffs result in stable periodic solutions, while heterogeneous distributions disrupt stable periodicity and lead to chaotic dynamics. Notably, increasing the initial density of cooperators, the rate of resource growth, and reducing the initial resource stock are favorable for sustaining cooperation. Interestingly, high payoffs for cooperators and low payoffs for defectors do not necessarily promote cooperative behavior, as evolutionary outcomes also depend on resource abundance. We provide the conditions that sustain cooperation, revealing the critical role of resource dynamics and spatial diffusion in shaping the evolution of cooperative strategies. Our findings have important implications for studying ecosystem management, conservation biology, and animal social behavior.

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.

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.

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.