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Register a new userGlobal dynamics of a two-strain flu model with a single vaccination and general incidence rate
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In this his paper, we studied the global dynamics of a two-strain flu model with a single-strain vaccine and general incidence rate. Four equilibrium points were obtained and the global dynamics of the model are completely determined via suitable lyapunov functions. We illustrate our results by some numerical simulations.
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A two-dimensional system of differential equations with delay modelling the glucose-insulin interaction processes in the human body is considered. Sufficient conditions are derived for the unique positive equilibrium in the system to be globally asymptotically stable. They are given in terms of the global attractivity of the fixed point in a limiting interval map. The existence of slowly oscillating periodic solutions is shown in the case when the equilibrium is unstable. The mathematical results are supported by extensive numerical simulations. It is shown that typical behaviour in the system is the convergence to either a stable periodic solution or to the unique stable equilibrium. The coexistence of several periodic solutions together with the stable equilibrium is demonstrated as a possibility.
In this paper, we consider a stochastic SIRS model with general incidence rate and perturbed by both white noise and color noise. We determine the threshold $lambda$ that is used to classify the extinction and permanence of the disease. In particular, $lambda<0$ implies that the disease-free $(K, 0, 0)$ is globally asymptotic stable, i.e., the disease will eventually disappear. If $lambda>0$ the epidemic is strongly stochastically permanent. Our result is considered as a significant generalization and improvement over the results in cite{HZ1, GLM1, LOK1, SLJJ1, ZJ1}.
This paper is concerned with the globally exponential stability of traveling wave fronts for a class of population dynamics model with quiescent stage and delay. First, we establish the comparison principle of solutions for the population dynamics model. Then, by the weighted energy method combining comparison principle, the globally exponential stability of traveling wave fronts of the population dynamics model under the quasi-monotonicity conditions is established.
We consider the so-called prion equation with the general incidence term introduced in [Greer et al., 2007], and we investigate the stability of the steady states. The method is based on the reduction technique introduced in [Gabriel, 2012]. The argument combines a recent spectral gap result for the growth-fragmentation equation in weighted $L^1$ spaces and the analysis of a nonlinear system of three ordinary differential equations.
A minimalistic model of the half-center oscillator is proposed. Within it, we consider dynamics of two excitable neurons interacting by means of the excitatory coupling. In the parameter space of the model, we identify the regions of dynamics, characteristic for central pattern generators: respectively, in-phase, anti-phase synchronous oscillations and quiescence, and study various bifurcation transitions between all these states. Suggested model can serve as a building block of specific complex central pattern generators for studies of rhythmic activity and information processing in animals and humans.
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