Allee effects on population dynamics with delay

Asymmetrical Impact of Allee Effect on a Discrete-Time Predator-Prey System

“…Here, an increase in stability refers to the case that the system with Allee effect approximates to the equilibrium point much faster than that without it. Clearly, in our system, Allee effects not only stabilize but also destabilize the population dynamics, which is in disagreement with previous work [10,14,[18][19][20][21]. The impact of the Allee effect on the stability of population models shows different dynamics when the corresponding model is difference.…”

“…Previous studies demonstrated that Allee effects play an important role in the stability analysis of equilibrium points of a population dynamics model. An Allee effect may have a stabilizing or a destabilizing effect on population dynamics [5,[7][8][9][10][11][12]14]. Even if the system is stable at an equilibrium point, the system subject to an Allee effect may reach its stable state in much longer time.…”

“…The effect usually saturates or vanishes as the population size gets larger. Although some work has shown that Allee effects might play a stabilizing and protective role [7][8][9][10], most studies have highlighted its negative impact on population persistence [4,5,[11][12][13][14].…”

A delayed eco-epidemiological system with infected prey and predator subject to the weak Allee effect

“…In this paper, we have consid-38 ered their model with the more realistic assumption that the predator 39 must take time delays to digest their food before having further ac- 40 tivities take place. In addition to the above assumption, we have con- 41 sidered that the predator population captures only infected prey who 42 on infected fish, on an average, is 31 times higher than the preda-66 tion rate on susceptible fish. This observation allows us to neglect 67 the predation on susceptible prey by predator.…”

“…Some 28 detailed arguments about the importance of time delays in practical 29 models can be found in the classical books [35,36,40]. As far as our 30 knowledge, there are very few works on the time delayed population 31 dynamics in the presence of Allee effect [41][42][43][44]. To the best of our 32 knowledge, the present work is the first attempt on the study of an 33 eco-epidemiological system under the influence of weak Allee effects 34 and time delay.…”