Bifurcation analysis of an SIRS epidemic model with a generalized nonmonotone and saturated incidence rate
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TLDR
A susceptible-infectious-recovered (SIRS) epidemic model with a generalized nonmonotone and saturated incidence rate is studied.About:
This article is published in Journal of Differential Equations.The article was published on 2019-07-15 and is currently open access. It has received 72 citations till now. The article focuses on the topics: Bogdanov–Takens bifurcation & Saddle-node bifurcation.read more
Citations
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Book
Differential Equations and Dynamical Systems
TL;DR: In this paper, the Third Edition of the Third edition of Linear Systems: Local Theory and Nonlinear Systems: Global Theory (LTLT) is presented, along with an extended version of the second edition.
Journal ArticleDOI
Dynamics in a simple evolutionary-epidemiological model for the evolution of an initial asymptomatic infection stage.
TL;DR: A simple epidemiological model with two infectious stages, where hosts in the first stage can be partially or fully asymptomatic, and proves the uniqueness of interior evolutionarily singular strategies for power-law and exponential trade-offs, which means bistability is always between zero and maximal latency.
Journal ArticleDOI
Global analysis in Bazykin's model with Holling II functional response and predator competition
Min Lu,Jicai Huang +1 more
TL;DR: In this article, a detailed bifurcation analysis of Bazykin's model with Holling II functional response and predator competition is presented, and sufficient conditions to guarantee the global asymptotical stability of the semi-trivial equilibrium or the unique positive equilibrium are also given.
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Global Dynamics of a Susceptible-Infectious-Recovered Epidemic Model with a Generalized Nonmonotone Incidence Rate.
TL;DR: It is shown that the basic reproduction number R 0 does not act as a threshold value for the disease spread anymore, and there exists a sub-threshold value R ∗ ( < 1) such that the disease-free equilibrium is globally asymptotically stable.
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Stability and Bifurcation in a Leslie-Gower Predator-Prey Model with Allee Effect
TL;DR: In this paper , a Leslie-Gower predator-prey model with Allee effect on the prey and a linear functional response was considered and the existence and stability of equilibria were analyzed.
References
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A contribution to the mathematical theory of epidemics
TL;DR: In this article, the authors considered the problem of finding a causal factor which appears to be adequate to account for the magnitude of the frequent epidemics of disease which visit almost every population.
A Contribution to the Mathematical Theory of Epidemics.
TL;DR: The present communication discussion will be limited to the case in which all members of the community are initially equally susceptible to the disease, and it will be further assumed that complete immunity is conferred by a single infection.
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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
Differential Equations and Dynamical Systems
TL;DR: In this paper, the Third Edition of the Third edition of Linear Systems: Local Theory and Nonlinear Systems: Global Theory (LTLT) is presented, along with an extended version of the second edition.
Journal ArticleDOI
A generalization of the Kermack-McKendrick deterministic epidemic model☆
Vincenzo Capasso,Gabriella Serio +1 more
TL;DR: In this article, the Kermack-McKendrick deterministic model is generalized, introducing an interaction term in which the dependence upon the number of infectives occurs via a nonlinear bounded function.
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