Journal of Biological Dynamics最新文献

In a recent study, a mathematically identical ODE model is derived from a multiscale PDE model of hepatitis C virus infection, which helps to overcome the limitations of the PDE model in the analysis. Here, an extended proposed model is formulated for this transformed ODE model by including the hepatocyte proliferation of both uninfected and infected cells. Unlike the transformed model, the proposed model can predict the triphasic viral decline and the virus level after therapy cessation without oscillations. Numerical simulations are performed to investigate the effect of hepatocyte proliferation and therapy with direct-acting antivirals agents (DAAs). The basic reproduction number is obtained, the equilibrium points are specified, and their stability is analysed. A bifurcation analysis is performed to specify the bifurcation points and to study the effect of varying system parameters. Various viral load profiles generated by the model are confirmed to fit with reported data in the literature.

We investigate the dynamics of a prey-predator model with cooperative hunting among specialist predators and maturation delay in predator growth. First, we consider a model without delay and explore the effect of hunting time on the coexistence of predator and their prey. When the hunting time is long enough and the cooperation rate among predators is weak, prey and predator species tend to coexist. Furthermore, we observe the occurrences of a series of bifurcations that depend on the cooperation rate and the hunting time. Second, we introduce a maturation delay for predator growth and analyse its impact on the system's dynamics. We find that as the delay becomes larger, predator species become more likely to go extinct, as the long maturation delay hinders the growth of the predator population. Our numerical exploration reveals that the delay causes shifts in both the bifurcation curves and bifurcation thresholds of the non-delayed system.

We consider different anti-symmetric Lotka-Volterra systems governing the pairwise interactions among the same n species inhabiting m spatially discrete habitat patches, with each patch having infinitely many equilibria. In the absence of inter-patch species migration, the species densities in each isolated patch evolve in periodic orbits. A central idea of this work is to design a control action to make the trajectories of the system asymptotically converge to a desired coexistence equilibrium among the infinitely many equilibrium points. We propose a scheme to simultaneously control different anti-symmetric Lotka-Volterra systems in multiple habitat patches by designing a metapopulation model. By introducing a suitable inter-patch migration of species, we prove that the trajectories of the resulting metapopulation model are effectively asymptotically converging to the desired coexistence equilibrium. The stability of the coexistence equilibrium is proved using Lyapunov methods coupled with LaSalle's invariance principle.

The work of Fred Brauer (1932-2021) broke new ground in several areas of mathematical population biology, especially mathematical epidemiology and population management. This special issue reflects his legacy: the lines of inquiry he opened, the impact of his research and his books, and his mentoring of generations of young researchers. This dedication highlights milestones in his career and connects his work to the contributions in this issue.

In this paper, we formulate a population suppression model and a population replacement model with periodic impulsive releases of Nilaparvata lugens infected with wStri. The conditions for the stability of wild-$N.lugens$-eradication periodic solution of two systems are obtained by applying the Floquet theorem and comparison theorem. And the sufficient conditions for the persistence in the mean of wild $N.lugens$ are also given. In addition, the sufficient conditions for the extinction and persistence of the wild $N.lugens$ in the subsystem without wLug are also obtained. Finally, we give numerical analysis which shows that increasing the release amount or decreasing the release period are beneficial for controlling the wild $N.lugens$, and the efficiency of population replacement strategy in controlling wild populations is higher than that of population suppression strategy under the same release conditions.

In volume transmission (or neuromodulation) neurons do not make one-to-one connections to other neurons, but instead simply release neurotransmitter into the extracellular space from numerous varicosities. Many well-known neurotransmitters including serotonin (5HT), dopamine (DA), histamine (HA), Gamma-Aminobutyric Acid (GABA) and acetylcholine (ACh) participate in volume transmission. Typically, the cell bodies are in one volume and the axons project to a distant volume in the brain releasing the neurotransmitter there. We introduce volume transmission and describe mathematically two natural homeostatic mechanisms. In some brain regions several neurotransmitters in the extracellular space affect each other's release. We investigate the dynamics created by this comodulation in two different cases: serotonin and histamine; and the comodulation of 4 neurotransmitters in the striatum and we compare to experimental data. This kind of comodulation poses new dynamical questions as well as the question of how these biochemical networks influence the electrophysiological networks in the brain.

In this paper, we investigate a reaction-diffusion model incorporating dynamic variables for nutrient, phytoplankton, and zooplankton. Moreover, we account for the impact of time delay in the growth of phytoplankton following nutrient uptake. Our theoretical analysis reveals that the time delay can trigger the emergence of persistent oscillations in the model via a Hopf bifurcation. We also analytically track the direction of Hopf bifurcation and the stability of the bifurcating periodic solutions. Our simulation results demonstrate stability switches occurring for the positive equilibrium with an increasing time lag. Furthermore, the model exhibits homogeneous periodic-2 and 3 solutions, as well as chaotic behaviour. These findings highlight that the presence of time delay in the phytoplankton growth can bring forth dynamical complexity to the nutrient-plankton system of aquatic habitats.