Hunting cooperation in a prey-predator model with maturation delay.

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.

Reconsideration of r/K Selection Theory Using Stochastic Control Theory and Nonlinear Structured Population Models.

Despite the fact that density effects and individual differences in life history are considered to be important for evolution, these factors lead to several difficulties in understanding the evolution of life history, especially when population sizes reach the carrying capacity. r/K selection theory explains what types of life strategies evolve in the presence of density effects and individual differences. However, the relationship between the life schedules of individuals and population size is still unclear, even if the theory can classify life strategies appropriately. To address this issue, we propose a few equations on adaptive life strategies in r/K selection where density effects are absent or present. The equations detail not only the adaptive life history but also the population dynamics. Furthermore, the equations can incorporate temporal individual differences, which are referred to as internal stochasticity. Our framework reveals that maximizing density effects is an evolutionarily stable strategy related to the carrying capacity. A significant consequence of our analysis is that adaptive strategies in both selections maximize an identical function, providing both population growth rate and carrying capacity. We apply our method to an optimal foraging problem in a semelparous species model and demonstrate that the adaptive strategy yields a lower intrinsic growth rate as well as a lower basic reproductive number than those obtained with other strategies. This study proposes that the diversity of life strategies arises due to the effects of density and internal stochasticity.

Threshold dynamics of an SIR epidemic model with hybrid of multigroup and patch structures.

In this paper, we formulate an SIR epidemic model with hybrid of multigroup and patch structures, which can be regarded as a model for the geographical spread of infectious diseases or a multi-group model with perturbation. We show that if a threshold value, which corresponds to the well-known basic reproduction number R0, is less than or equal to unity, then the disease-free equilibrium of the model is globally asymptotically stable. We also show that if the threshold value is greater than unity, then the model is uniformly persistent and has an endemic equilibrium. Moreover, using a Lyapunov functional technique, we obtain a sufficient condition under which the endemic equilibrium is globally asymptotically stable. The sufficient condition is satisfied if the transmission coefficients in the same groups are large or the per capita recovery rates are small.

Global stability for a class of discrete SIR epidemic models.

In this paper, we propose a class of discrete SIR epidemic models which are derived from SIR epidemic models with distributed delays by using a variation of the backward Euler method. Applying a Lyapunov functional technique, it is shown that the global dynamics of each discrete SIR epidemic model are fully determined by a single threshold parameter and the effect of discrete time delays are harmless for the global stability of the endemic equilibrium of the model.