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An introduction to structured population dynamics
TLDR
In this paper, the authors present a case study of multispecies interactions with continuous models of age-structured models and show that these models can be used in a variety of applications.Abstract:
Preface 1 Discrete Models Matrix Models Autonomous Single Species Models Some Applications A Case Study Multispecies Interactions 2 Continuous Models Age-Structured Models Autonomous Age-Structured Models Some Applications Multispecies Interactions Other Structured Models 3 Population Level Dynamics Ergodicity and Nonlinear Models The Linear Chain Trick Hierarchical Models Total Population Size in Age-Structured Models Appendix A Stability Theory for Maps Linear Maps Linearization of Maps Appendix B Bifurcation Theorems A Global Bifurcation Theorem Local Parameterization Appendix C Miscellaneous Proofs Bibliography Indexread more
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A beginners guide to adaptive dynamics
TL;DR: The aim of these notes is to illustrate, largely by way of examples, how standard ecological models can be put into an evolutionary perspective in order to gain insight in the role of natural selection in shaping life history characteristics.
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Relations between deterministic and stochastic thresholds for disease extinction in continuous- and discrete-time infectious disease models.
TL;DR: Through relations between branching process theory and the corresponding deterministic model, it is shown that the deterministic and stochastic thresholds are in agreement for discrete-time and continuous-time infectious disease models with multiple infectious groups.
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Consequences of an allee effect in the invasion of a pacific estuary by spartina alterniflora
TL;DR: The deterministic model demonstrates a novel way of representing density dependence and an Allee effect in population biology and could be applied to model the population dynamics of any species that spreads from multiple foci and in which these foci later coalesce.
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Dynamics of an age-of-infection cholera model
TL;DR: A new model for the dynamics of cholera is formulated that incorporates both the infection age of infectious individuals and biological age of pathogen in the environment, and the basic reproduction number is defined and proved to be a sharp threshold determining whether or not cholERA dies out.
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Numerical solution of predator-prey model with Beddington-DeAngelis functional response and fractional derivatives with Mittag-Leffler kernel.
Behzad Ghanbari,Devendra Kumar +1 more
TL;DR: It is shown first that the fractional predator-prey model has a unique solution, then an efficient numerical scheme based on the product integration rule is proposed that is in excellent agreement with the expected theoretical results.