Displaying similar documents to “A simple mathematical model for Batesian mimicry.”

Bifurcation and control for a discrete-time prey-predator model with Holling-IV functional response

Qiaoling Chen, Zhidong Teng, Zengyun Hu (2013)

International Journal of Applied Mathematics and Computer Science

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The dynamics of a discrete-time predator-prey model with Holling-IV functional response are investigated. It is shown that the model undergoes a flip bifurcation, a Hopf bifurcation and a saddle-node bifurcation by using the center manifold theorem and bifurcation theory. Numerical simulations not only exhibit our results with the theoretical analysis, but also show the complex dynamical behaviors, such as the period-3, 6, 9, 12, 20, 63, 70, 112 orbits, a cascade of period-doubling bifurcations...

On the dynamics of a vaccination model with multiple transmission ways

Shu Liao, Weiming Yang (2013)

International Journal of Applied Mathematics and Computer Science

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In this paper, we present a vaccination model with multiple transmission ways and derive the control reproduction number. The stability analysis of both the disease-free and endemic equilibria is carried out, and bifurcation theory is applied to explore a variety of dynamics of this model. In addition, we present numerical simulations to verify the model predictions. Mathematical results suggest that vaccination is helpful for disease control by decreasing the control reproduction number...

Memory Effects in Population Dynamics : Spread of Infectious Disease as a Case Study

A. Pimenov, T.C. Kelly, A. Korobeinikov, M.J.A. O’Callaghan, A.V. Pokrovskii, D. Rachinskii (2012)

Mathematical Modelling of Natural Phenomena

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Modification of behaviour in response to changes in the environment or ambient conditions, based on memory, is typical of the human and, possibly, many animal species.One obvious example of such adaptivity is, for instance, switching to a safer behaviour when in danger, from either a predator or an infectious disease. In human society such switching to safe behaviour is particularly apparent during epidemics. Mathematically, such changes...