Dynamics of a stochastic epidemic model with quarantine and non-monotone incidence
Tingting Wang,Shulin Sun +1 more
TLDR
In this paper , a stochastic SIQR epidemic model with non-monotone incidence is investigated, where the disease-free equilibrium of the deterministic model is globally asymptotically stable by using the Lyapunov method.Abstract:
In this paper, a stochastic SIQR epidemic model with non-monotone incidence is investigated. First of all, we consider the disease-free equilibrium of the deterministic model is globally asymptotically stable by using the Lyapunov method. Secondly, the existence and uniqueness of positive solution to the stochastic model is obtained. Then, the sufficient condition for extinction of the stochastic model is established. Furthermore, a unique stationary distribution to stochastic model will exist by constructing proper Lyapunov function. Finally, numerical examples are carried out to illustrate the theoretical results, with the help of numerical simulations, we can see that the higher intensities of the white noise or the bigger of the quarantine rate can accelerate the extinction of the disease. This theoretically explains the significance of quarantine strength (or isolation measures) when an epidemic erupts.read more
References
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Journal ArticleDOI
A familial cluster of pneumonia associated with the 2019 novel coronavirus indicating person-to-person transmission: a study of a family cluster.
Jasper Fuk-Woo Chan,Shuofeng Yuan,Kin-Hang Kok,Kelvin K. W. To,Kelvin K. W. To,Hin Chu,Jin Yang,Fanfan Xing,Jieling Liu,Cyril C. Y. Yip,Rosana W.S. Poon,Hoi Wah Tsoi,Simon Kam Fai Lo,Kwok-Hung Chan,Vincent Kwok-Man Poon,Wan Mui Chan,Jonathan Daniel Ip,Jian Piao Cai,Vincent C.C. Cheng,Honglin Chen,Honglin Chen,Christopher K.M. Hui,Kwok-Yung Yuen +22 more
TL;DR: The findings are consistent with person-to-person transmission of this novel coronavirus in hospital and family settings, and the reports of infected travellers in other geographical regions.
Journal ArticleDOI
An Algorithmic Introduction to Numerical Simulation of Stochastic Differential Equations
TL;DR: The article is built around $10$ MATLAB programs, and the topics covered include stochastic integration, the Euler--Maruyama method, Milstein's method, strong and weak convergence, linear stability, andThe stochastics chain rule.
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.
Journal ArticleDOI
Dynamical behavior of an epidemic model with a nonlinear incidence rate
Shigui Ruan,Wendi Wang +1 more
TL;DR: In this article, the global dynamics of an epidemic model with vital dynamics and nonlinear incidence rate of saturated mass action was studied and it was shown that either the number of infective individuals tends to zero as time evolves or there is a region such that the disease will be persistent if the initial position lies in the region and the disease would disappear if the starting position lies outside this region.
Journal ArticleDOI
Global analysis of an epidemic model with nonmonotone incidence rate.
Dongmei Xiao,Shigui Ruan +1 more
TL;DR: It is shown that either the number of infective individuals tends to zero as time evolves or the disease persists.
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