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In this research, we study the impacts of the traceable mobility in a two-patch environment when the population in each patch exhibits strong Allee effects. Traveling individuals are traced across patches by budgeting the average time spent in each patch while keeping their place of residency. Particularly, we focus on the impact that the effective population (residents and visitors) produces on regional dynamics.Our results show that low mobility across regions produces simple dynamics, where orbits converge to single or double extinction, or to a coexistence steady state. We derive mobility conditions under which an endangered population may benefit of the presence of a visitant one and avoid extinction -- the rescue effect. Nonetheless, increments in the visiting population would also lead the resident population to extinction -- the induced extinction effect.

 

The quarantine strategy plays a crucial role in the prevention and control of infectious disease. In this paper, a two-layer network model coupling the transmission of infectious diseases and the dynamics of human behavior based on game theory is proposed. The basic reproduction number of the infectious disease in our proposed model is obtained by the next-generation matrix method and the stability of the disease-free equilibrium is analyzed. Theoretical results show that the spread of infectious diseases can be controlled when the voluntary quarantined individuals reach a certain proportion. The sensitivities of the parameters are analyzed by simulations, and the results show that increasing propaganda can directly accelerate quarantine, and reducing the relative cost of quarantine has a significant effect on preventing the infectious diseases. Increasing the detection rate will lead to overestimating the proportion of undiagnosed infected individuals, and can also promote individuals to quarantine.

 

The variation of nutrient supply not only leads to the differences in the phytoplankton biomass and primary productivity but also induces the long-term phenotypic evolution of phytoplankton. It is widely accepted that marine phytoplankton follows Bergmann's Rule and becomes smaller with climate warming. Compared with the direct effect of increasing temperature, the indirect effect via nutrient supply is considered to be an important and dominant factor in the reduction of phytoplankton cell size. In this paper, a size-dependent nutrient-phytoplankton model is developed to explore the effects of nutrient supply on the evolutionary dynamics of functional traits associated with phytoplankton size. The ecological reproductive index is introduced to investigate the impacts of input nitrogen concentration and vertical mixing rate on the persistence of phytoplankton and the distribution of cell size. In addition, by applying the adaptive dynamics theory, we study the relationship between nutrient input and the evolutionary dynamics of phytoplankton. The results show that input nitrogen concentration and vertical mixing rate have significant effects on the cell size evolution of phytoplankton. Specifically, cell size tends to increase with the input nutrient concentration, as does the diversity of cell sizes. In addition, a single-peaked relationship between vertical mixing rate and cell size is observed. When the vertical mixing rate is too low or too high, only small individuals are dominant in the water column. When the vertical mixing rate is moderate, large individuals can coexist with small individuals, so the diversity of phytoplankton is elevated. We predict that reduced intensity of nutrient input due to climate warming will lead to a trend towards smaller cell size and will reduce the diversity of phytoplankton.

 

In this paper, we investigate the dynamical behavior for a hybrid non-autonomous predator–prey system with Holling Type II functional response, impulsive effects and generalist predator on time scales, where our proposed model commutes between a continuous-time dynamical system and discrete-time dynamical system. By using comparison theorems, we first study the permanence results of the proposed model. Also, we established the uniformly asymptotic stability for the almost periodic solution of the proposed model. Finally, in the last section, we provide some examples with numerical simulation.