Journal of Biological Dynamics最新文献

In this paper, we develop discrete models of Tuberculosis (TB). This includes SEI endogenous and exogenous models without treatment. These models are then extended to a SEIT model with treatment. We develop two types of net reproduction numbers, one is the traditional $R_0$ which is based on the disease-free equilibrium, and a new net reproduction number $R_0\left(E^{\ast }\right)$ based on the endemic equilibrium. It is shown that the disease-free equilibrium is globally asymptotically stable if $R_0\le 1$ and unstable if $R_0>1$. Moreover, the endemic equilibrium is locally asymptotically stable if $R_0\left(E^{\ast }\right)<1<R_0$.

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.

A stochastic mathematical model is proposed to study how environmental heterogeneity and the augmentation of mosquitoes with $Wolbachia$ bacteria affect the outcomes of dengue disease. The existence and uniqueness of the positive solutions of the system are studied. Then the V-geometrically ergodicity and stochastic ultimate boundedness are investigated. Further, threshold conditions for successful population replacement are derived and the existence of a unique ergodic steady-state distribution of the system is explored. The results show that the ratio of infected to uninfected mosquitoes has a great influence on population replacement. Moreover, environmental noise plays a significant role in control of dengue fever.