13,997 research outputs found
Stability analysis of delayed SIR epidemic models with a class of nonlinear incidence rates
We analyze stability of equilibria for a delayed SIR epidemic model, in which population growth is subject to logistic growth in absence of disease, with a nonlinear incidence rate satisfying suitable monotonicity conditions. The model admits a unique endemic equilibrium if and only if the basic reproduction number R 0 exceeds one, while the trivial equilibrium and the disease-free equilibrium always exist. First we show that the disease-free equilibrium is globally asymptotically stable if and only if R 0 ≤ 1. Second we show that the model is permanent if and only if R 0 > 1. Moreover, using a threshold parameter R 0 characterized by the nonlinear incidence function, we establish that the endemic equilibrium is locally asymptotically stable for 1< R0≤R 0 and it loses stability as the length of the delay increases past a critical value for 1<R 0< R0. Our result is an extension of the stability results in [J.-J. Wang, J.-Z. Zhang, Z. Jin, Analysis of an SIR model with bilinear incidence rate, Nonlinear Anal. RWA 11 (2009) 2390-2402]
Stochastic epidemic SEIRS models with a constant latency period
In this paper we consider the stability of a class of deterministic and
stochastic SEIRS epidemic models with delay. Indeed, we assume that the
transmission rate could be stochastic and the presence of a latency period of
consecutive days, where is a fixed positive integer, in the "exposed"
individuals class E. Studying the eigenvalues of the linearized system, we
obtain conditions for the stability of the free disease equilibrium, in both
the cases of the deterministic model with and without delay. In this latter
case, we also get conditions for the stability of the coexistence equilibrium.
In the stochastic case we are able to derive a concentration result for the
random fluctuations and then, using the Lyapunov method, that under suitable
assumptions the free disease equilibrium is still stable
Stability and bifurcations in an epidemic model with varying immunity period
An epidemic model with distributed time delay is derived to describe the
dynamics of infectious diseases with varying immunity. It is shown that
solutions are always positive, and the model has at most two steady states:
disease-free and endemic. It is proved that the disease-free equilibrium is
locally and globally asymptotically stable. When an endemic equilibrium exists,
it is possible to analytically prove its local and global stability using
Lyapunov functionals. Bifurcation analysis is performed using DDE-BIFTOOL and
traceDDE to investigate different dynamical regimes in the model using
numerical continuation for different values of system parameters and different
integral kernels.Comment: 16 pages, 5 figure
Analysis of a stochastic distributed delay epidemic model with relapse and Gamma distribution kernel
In this work, we investigate a stochastic epidemic model with relapse and distributed delay. First, we prove that our model possesses and unique global positive solution. Next, by means of the Lyapunov method, we determine some sufficient criteria for the extinction of the disease and its persistence. In addition, we establish the existence of a unique stationary distribution to our model. Finally, we provide some numerical simulations for the stochastic model to assist and show the applicability and efficiency of our results.Ministerio de Ciencia, Innovación y Universidades (MICINN). EspañaEuropean Commission (EC). Fondo Europeo de Desarrollo Regional (FEDER
Time scales of epidemic spread and risk perception on adaptive networks
Incorporating dynamic contact networks and delayed awareness into a contagion
model with memory, we study the spreading patterns of infectious diseases in
connected populations. It is found that the spread of an infectious disease is
not only related to the past exposures of an individual to the infected but
also to the time scales of risk perception reflected in the social network
adaptation. The epidemic threshold is found to decrease with the rise
of the time scale parameter s and the memory length T, they satisfy the
equation .
Both the lifetime of the epidemic and the topological property of the evolved
network are considered. The standard deviation of the degree
distribution increases with the rise of the absorbing time , a power-law
relation is found
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