4 research outputs found
Dynamics for a stochastic delayed SIRS epidemic model
In this paper, we consider a stochastic delayed SIRS epidemic model with seasonal variation. Firstly, we prove that the system is mathematically and biologically well-posed by showing the global existence, positivity and stochastically ultimate boundneness of the solution. Secondly, some sufficient conditions on the permanence and extinction of the positive solutions with probability one are presented. Thirdly, we show that the solution of the system is asymptotical around of the disease-free periodic solution and the intensity of the oscillation depends of the intensity of the noise. Lastly, the existence of stochastic nontrivial periodic solution for the system is obtained
Dynamics and simulations of stochastic COVID-19 epidemic model using Legendre spectral collocation method
The aim of this study is to investigate the dynamics of epidemic transmission of COVID-19 SEIR stochastic model with generalized saturated incidence rate. We assume that the random perturbations depends on white noises, which implies that it is directly proportional to the steady states. The existence and uniqueness of the positive solution along with the stability analysis is provided under disease-free and endemic equilibrium conditions for asymptotically stable transmission dynamics of the model. An epidemiological metric based on the ratio of basic reproduction is used to describe the transmission of an infectious disease using different parameters values involve in the proposed model. A higher order scheme based on Legendre spectral collocation method is used for the numerical simulations. For the better understanding of the proposed scheme, a comparison is made with the deterministic counterpart. In order to confirm the theoretical analysis, we provide a number of numerical examples
Analysis of a stochastic Leslie-Gower three-species food chain system with Holling-II functional response and Ornstein-Uhlenbeck process
This paper studies a stochastic Leslie-Gower model with a Holling-II functional response that is driven by the Ornstein-Uhlenbeck process. Some asymptotic properties of the solution of the stochastic Leslie-Gower model are introduced: The existence and uniqueness of the global solution of the model are given; the ultimate boundedness of the model is proven; by constructing the Lyapunov function and applying Ito's formula, the existence of the stationary distribution of the model is demonstrated; and the conditions for system extinction are discussed. Finally, numerical simulations are used to validate our conclusion
The stochastic extinction and stability conditions for a class of malaria epidemic models
The stochastic extinction and stability in the mean of a family of SEIRS
malaria models with a general nonlinear incidence rate is presented. The
dynamics is driven by independent white noise processes from the disease
transmission and natural death rates. The basic reproduction number
, the expected survival probability of the plasmodium
, and other threshold values are calculated.
A sample Lyapunov exponential analysis for the system is utilized to obtain
extinction results. Moreover, the rate of extinction of malaria is estimated,
and innovative local Martingale and Lyapunov functional techniques are applied
to establish the strong persistence, and asymptotic stability in the mean of
the malaria-free steady population. %The extinction of malaria depends on
, and . Moreover, for either
, or ,
whenever , respectively, extinction of malaria occurs.
Furthermore, the robustness of these threshold conditions to the intensity of
noise from the disease transmission rate is exhibited. Numerical simulation
results are presented.Comment: arXiv admin note: substantial text overlap with arXiv:1808.09842,
arXiv:1809.03866, arXiv:1809.0389