A discrete predator-prey system with age-structure for predator and natural barriers for prey

Tang, Sanyi; Chen, Lansun

doi:10.1051/m2an:2001102

Cited by 11 publications

(12 citation statements)

References 24 publications

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“…[74] The system of equations (7)-(14) is strongly persistent at time τ if for each t =0,1,2,⋯ τ .The system of equations (7)-(14) is weakly persistent at time τ if for each t =0,1,2,⋯ τ −1 and , D τ + P t + Q τ + V τ ,>0 and T τ >0.The system of equations (7)-(14) is strongly persistent if it is strongly persistent at time τ for τ =0,1,2⋯ and .The system of equations (7)-(14) is uniformly persistent if it is strongly persistent at time τ for τ =0,1,2⋯ and there exist a positive constant ϖ such that .The system of equations (7)-(14) is permanent if it is uniform persistent and point dissipative.…”

Section: Methodsmentioning

confidence: 99%

A comparison of elasticities of viral levels to specific immune response mechanisms in human immunodeficiency virus infection

et al. 2014

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BackgroundThe presence of an asymptomatic phase in an HIV infection indicates that the immune system can partially control the infection. Determining the immune mechanisms that contribute significantly to the partial control of the infection enhance the HIV infection intervention strategies and is important in vaccine development. Towards this goal, a discrete time HIV model, which incorporates the life cycle aspects of the virus, the antibody (humoral) response and the cell-mediated immune response is formulated to determine immune system components that are most efficient in controlling viral levels. Ecological relationships are used to model the interplay between the immune system components and the HIV pathogen. Model simulations and transient elasticity analysis of the viral levels to immune response parameters are used to compare the different immune mechanisms.ResultsIt is shown that cell-mediated immune response is more effective in controlling the viral levels than the antibody response. Killing of infected cells is shown to be crucial in controlling the viral levels. Our results show a negative correlation between the antibody response and the viral levels in the early stages of the infection, but we predicted this immune mechanism to be positively correlated with the viral levels in the late stage of the infection. A result that suggests lack of relevance of antibody response with infection progression. On the contrary, we predicted the cell-mediated immune response to be always negatively correlated with viral levels.ConclusionNeutralizing antibodies can only control the viral levels in the early days of the HIV infection whereas cell-mediated immune response is beneficial during all the stages of the infection. This study predicts that vaccine design efforts should also focus on stimulating killer T cells that target infected cells.Electronic supplementary materialThe online version of this article (doi:10.1186/1756-0500-7-737) contains supplementary material, which is available to authorized users.

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Section: Methodsmentioning

confidence: 99%

A comparison of elasticities of viral levels to specific immune response mechanisms in human immunodeficiency virus infection

et al. 2014

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“…Именно наличие этих временных отставаний (которые позволяют учесть ненулевую скорость трансформации биомассы потребленных жертв в хищников), по всей видимости, представляет собой фундаментальное различие между дискретными и непрерывными по времени моделями типа «хищник -жертва» [10,16]. В работах, посвященных изучению динамики системы «хищник -жертва» с учетом возрастной детализации или стадий развития, используются в основном модели с непрерывным временем [25][26][27][28], при этом системы с дискретным временем применяются реже [12,[29][30][31][32][33]. В частности, можно выделить работы, в которых рассматривается влияние возрастной структуры либо хищника [25,32,34], либо жертвы [31,35] на развитие сообщества [36].…”

Section: Introductionunclassified

Bistability and Bifurcations in Modified Nicholson-Bailey Model with Age-Structure for Prey

Revutskaya¹,

Кулаков²,

Frisman³

2019

Math.Biol.Bioinf.

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The paper investigates dynamic modes of the predator-prey model with age structure for prey. We use a slight modification of the Nicholson-Bailey model to describe the interaction between predator and prey. We assume the population size is regulated by decreasing juvenile survival rate with growth of age class sizes. Conditions for sustainable coexistence of interacting species are described. It is shown that the coexistence of species becomes possible if there are a transcritical or saddle-node (tangential) bifurcations. Due to the saddle-node bifurcation there is bistability in the system of interacting species: predator either coexists with prey or dies depending on the initial conditions. It is shown that the range of demographic parameters, for which the prey and predator coexist, can significantly increase with growth of survival of adult prey or the proportion of predators born or the prey consumption rate of the predator. We studied the oscillation scenarios of interacting population, influences of reproduction, survival and self-regulation rates of population prey and age-dependent predation as well as variations in the current number on transitions between different dynamic modes. It is shown that an increase in the birth rate of the prey under intraspecific competition can lead to a dynamics destabilization and to oscillations appearance in numbers. Age-dependent predation is shown to be a stabilizing influence. At the same time, with a high birth rate of the prey, the system stability is ensured by the high survival rate of adult prey. It was found that in the model parametric space, both bistability and multistability arises, which are not related to each other. Consequently, even a small variation of the current population size leads to more complex behavior of the interacting species, and can give a significant change in both the observed dynamic mode and the coexistence scenario of the species.

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“…Complexity of different type has been explained extendedly through some important articles [6,13,20,21] A complex system exhibits some (and possibly all) of the following characteristics:…”

Section: Introductionmentioning

confidence: 99%

Complexity Studies in Some Piecewise Continuous Dynamical Systems

Chitkara

Kumra

Saha

2016

MJIS

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The, "Complex systems", stands as a broad term for many diverse disciplines of science and engineering including natural & medical sciences. Complexities appearing in various dynamical systems during evolution are now interesting subjects of studies. Chaos appearing in various dynamical systems can also be viewed as a form of complexity. For some cases nonlinearities within the systems and for other cases piecewise continuity property of the system are responsible for such complexity. Dynamical systems represented by mathematical models having piecewise continuous properties show strange complexity character during evolution. Interesting recent articles explain widely on complexities in various systems. Observable quantities for complexity are measurement of Lyapunov exponents (LCEs), topological entropies, correlation dimension etc.The present article is related to study of complexity in systems having piecewise continuous properties. Some mathematical models are considered here in this regard including famous Lozi map, a discrete mathematical model and Chua circuit, a continuous model. Investigations have been carried forward to obtain various attractors of these maps appearing during evolution in diverse and interesting pattern for different set of values of parameters and for different initial conditions. Numerical investigations extended to obtain bifurcation diagrams, calculations of LCEs, topological entropies and correlation dimension together with their graphical representation.

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A discrete predator-prey system with age-structure for predator and natural barriers for prey

Cited by 11 publications

References 24 publications

A comparison of elasticities of viral levels to specific immune response mechanisms in human immunodeficiency virus infection

A comparison of elasticities of viral levels to specific immune response mechanisms in human immunodeficiency virus infection

Bistability and Bifurcations in Modified Nicholson-Bailey Model with Age-Structure for Prey

Complexity Studies in Some Piecewise Continuous Dynamical Systems

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