A Qualitative Study of Mathematical Models of Population Dynamics

1991 ◽  
pp. 403-409
Author(s):  
V. M. Tikhomirov
Keyword(s):  
Population Dynamics ◽  
Qualitative Study ◽  
Mathematical Models

Modeling virus pandemics in a globally connected world a challenge towards a mathematics for living systems

2021 ◽  
pp. 1-7
Author(s):  
N. Bellomo ◽  
F. Brezzi ◽  
M. A. J. Chaplain
Keyword(s):  
Complex System ◽  
Population Dynamics ◽  
Mathematical Models ◽  
Modeling And Simulation ◽  
Critical Analysis ◽  
Living Systems ◽  
Special Issue ◽  
Research Perspectives ◽  
Heterogeneous Features

This editorial paper presents the papers published in a special issue devoted to the modeling and simulation of mutating virus pandemics in a globally connected world. The presentation is proposed in three parts. First, motivations and objectives are presented according to the idea that mathematical models should go beyond deterministic population dynamics by considering the multiscale, heterogeneous features of the complex system under consideration. Subsequently, the contents of the papers in this issue are presented referring to the aforementioned complexity features. Finally, a critical analysis of the overall contents of the issue is proposed, with the aim of providing a forward look to research perspectives.

scholarly journals Lie Symmetries and Solutions of Reaction Diffusion Systems Arising in Biomathematics

Symmetry ◽  
2021 ◽  
Vol 13 (8) ◽  
pp. 1530
Author(s):  
Mariano Torrisi ◽  
Rita Traciná
Keyword(s):  
Population Dynamics ◽  
Mathematical Models ◽  
Lie Algebra ◽  
Reaction Diffusion ◽  
Equivalence Transformation ◽  
Transformation Groups ◽  
Weak Equivalence ◽  
Reaction Diffusion Systems ◽  
Diffusion Systems ◽  
Special Solutions

In this paper, a special subclass of reaction diffusion systems with two arbitrary constitutive functions Γ(v) and H(u,v) is considered in the framework of transformation groups. These systems arise, quite often, as mathematical models, in several biological problems and in population dynamics. By using weak equivalence transformation the principal Lie algebra, LP, is written and the classifying equations obtained. Then the extensions of LP are derived and classified with respect to Γ(v) and H(u,v). Some wide special classes of special solutions are carried out.

scholarly journals Parasites that change predator or prey behaviour can have keystone effects on community composition

2014 ◽  
Vol 10 (1) ◽  
pp. 20130879 ◽  
Author(s):  
Melanie J. Hatcher ◽  
Jaimie T. A. Dick ◽  
Alison M. Dunn
Keyword(s):  
Population Dynamics ◽  
Community Structure ◽  
Mathematical Models ◽  
Biological Invasions ◽  
Intraguild Predation ◽  
Host Species ◽  
Indirect Interactions ◽  
Ecological Impacts ◽  
Mediated Effects ◽  
Population Interactions

Parasites play pivotal roles in structuring communities, often via indirect interactions with non-host species. These effects can be density-mediated (through mortality) or trait-mediated (behavioural, physiological and developmental), and may be crucial to population interactions, including biological invasions. For instance, parasitism can alter intraguild predation (IGP) between native and invasive crustaceans, reversing invasion outcomes. Here, we use mathematical models to examine how parasite-induced trait changes influence the population dynamics of hosts that interact via IGP. We show that trait-mediated indirect interactions impart keystone effects, promoting or inhibiting host coexistence. Parasites can thus have strong ecological impacts, even if they have negligible virulence, underscoring the need to consider trait-mediated effects when predicting effects of parasites on community structure in general and biological invasions in particular.

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