Journal ArticleDOI
Bifurcation of a predator–prey model with disease in the prey
Xuanliang Liu,Chaoyang Wang +1 more
TLDR
In this article, a predator-prey model with disease in the prey is considered, and the dynamics of the model in terms of local analysis of equilibria and bifurcation analysis of a boundary equilibrium and a positive equilibrium are studied.Abstract:
In this paper, a predator–prey model with disease in the prey is considered. Assume that the predator eats only the infected prey, and the incidence rate is nonlinear. We study the dynamics of the model in terms of local analysis of equilibria and bifurcation analysis of a boundary equilibrium and a positive equilibrium. We discuss the Bogdanov–Takens bifurcation near the boundary equilibrium and the Hopf bifurcation near the positive equilibrium; numerical simulation results are given to support the theoretical predictions.read more
Citations
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Journal ArticleDOI
Numerical solution of fractional order smoking model via laplace Adomian decomposition method
TL;DR: In this article, the authors deal with the dynamics of giving up smoking model of fractional order with the help of Laplace transformation and obtain the solution of the model in form of infinite series.
Journal ArticleDOI
A mathematical study of a prey–predator model in relevance to pest control
Soovoojeet Jana,Tapan Kumar Kar +1 more
TL;DR: In this article, an ecological system consisting of pest and its natural enemy as predator is proposed and analyzed in a systemic manner, study the dependence of the dynamics on some vital parameters and discuss the global behavior and controllability of the proposed system.
Journal ArticleDOI
Complex dynamics of an eco-epidemiological model with different competition coefficients and weak Allee in the predator
TL;DR: In this article, the authors consider a predator-prey model with type II functional response and consider different competition coefficients within the prey population, which leads to the emergent carrying capacity.
Journal ArticleDOI
Bifurcation analysis in a predator–prey system with a functional response increasing in both predator and prey densities
TL;DR: In this paper, a qualitative study of a predator-prey interaction system with the functional response proposed by Cosner et al. is presented, which describes a behavioral mechanism which a group of predators foraging in linear formation searches, contacts and then hunts a school of prey.
Journal ArticleDOI
Hopf Bifurcation and Hybrid Control of a Delayed Ecoepidemiological Model with Nonlinear Incidence Rate and Holling Type II Functional Response
TL;DR: In this paper, a hybrid control strategy is proposed to postpone the onset of an inherent bifurcation of the system by utilizing normal form method and center manifold theorem, the explicit formulas that determine the direction of Hopf bifurbcation and the stability of bifurlating period solutions of the controlled system are derived.
References
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Book
Infectious Diseases of Humans: Dynamics and Control
Roy M. Anderson,Robert M. May +1 more
TL;DR: This book discusses the biology of host-microparasite associations, dynamics of acquired immunity heterogeneity within the human community indirectly transmitted helminths, and the ecology and genetics of hosts and parasites.
Journal ArticleDOI
The Mathematics of Infectious Diseases
TL;DR: Threshold theorems involving the basic reproduction number, the contact number, and the replacement number $R$ are reviewed for classic SIR epidemic and endemic models and results with new expressions for $R_{0}$ are obtained for MSEIR and SEIR endemic models with either continuous age or age groups.
Book
Elements of applied bifurcation theory
TL;DR: One-Parameter Bifurcations of Equilibria in continuous-time systems and fixed points in Discrete-Time Dynamical Systems have been studied in this paper, where they have been used for topological equivalence and structural stability of dynamical systems.
Journal ArticleDOI
Influence of nonlinear incidence rates upon the behavior of SIRS epidemiological models
TL;DR: When the traditional assumption that the incidence rate is proportional to the product of the numbers of infectives and susceptibles is dropped, the SIRS model can exhibit qualitatively different dynamical behaviors, including Hopf bifurcations, saddle-node bifuriations, and homoclinic loop bifURcations.
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