Global Attractivity in a Predator–prey System With Pure Delays

Tang, Xianhua; Zou, Xingfu

doi:10.1017/s0013091506000988

Cited by 8 publications

(3 citation statements)

References 24 publications

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“…Second, the Campbell (1961) is so mathematically challenging that its use is impractical in biology. How to mathematically analyze a system of nonlinear delay-differential equations is an ongoing subject of research in applied mathematics (Tang and Zou 2008, Huang et. al.…”

Section: Terminologymentioning

confidence: 99%

Lytic/Lysogenic Transition as a Life-History Switch

Roughgarden

2023

Preprint

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A critique of the delay-differential equation model of Cambell (1961) for the population dynamics of virulent phage and bacteria reveals the need for a new model. This paper introduces a new and simple model for the population dynamics of phage and bacteria that features infection of bacteria by Poisson sampling of viral particles from the environment and is developed in discrete time with a time step equal to the viral latency time Density-dependent burst size does not lead to virus-bacteria coexistence whereas density-dependent viral absorption onto the bacterial surface is sufficient to produce virulent virus-bacteria coexistence. The condition for transition from a lytic to lysogenic phase is derived as a ``switch function''. The virus switches from lytic to lysogenic when its population grows faster with prophage than with separate virions produced by lysis of the infected cell. The switch function predicts temperate viral-bacteria dynamics in several environmental scenarios including environmental enrichment leading to microbialization, fluctuating environmental conditions that promote horizontal gene transfer (HGT), and the integration of prophage-containing bacteria into the microbiome of a eukaryotic host forming a functionally integrated tripartite holobiont.

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Section: Terminologymentioning

confidence: 99%

Lytic/Lysogenic Transition as a Life-History Switch

Roughgarden

2023

Preprint

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“…In [6], the authors presented a stage-structured predator prey model with gestation delay. A delay prey-predator system without instantaneous negative feedback has been studied in [32]. The authors in [37] considered a class of delayed Lokta-Volterra prey-predator model with two delays.…”

mentioning

confidence: 99%

“…Time series P 2 (t) and Z 2 (t) of system (2) with parameters and functions given in(30),(32) and(33).…”

mentioning

confidence: 99%

A prey-predator model with migrations and delays

Al-Darabsah¹,

Tang²,

Yuan³

2016

DCDS-B

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In this paper we propose a prey-predator model in multiple patches through the stage structured maturation time delay with migrations among patches. Focus on the case with two patches, we discuss the existence of equilibrium points and the uniform persistence. In particular, when the maturation times are the same in the patches, we study the local and global attractivity of boundary equilibrium point with general migration function and the local stability of the positive equilibrium with constant migration rate. Numerical simulations are provided to demonstrate the theoretical results, to illustrate the effect of the maturation time, the migration rate on the dynamical behavior of the system.

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