scholarly journals Global stability of a multistrain SIS model with superinfection

2016 ◽  
Vol 13 (6) ◽  
pp. 4-4
Author(s):  
Attila Dénes ◽  
Yoshiaki Muroya ◽  
Gergely Röst
Keyword(s):  
Global Stability ◽  
Sis Model

scholarly journals Global stability of a multistrain SIS model with superinfection and patch structure

2020 ◽  
Vol 43 (17) ◽  
pp. 9671-9680
Author(s):  
Attila Dénes ◽  
Yoshiaki Muroya ◽  
Gergely Röst
Keyword(s):  
Global Stability ◽  
Sis Model ◽  
Patch Structure

Global stability and positive recurrence of a stochastic SIS model with Lévy noise perturbation

2019 ◽  
Vol 523 ◽  
pp. 677-690 ◽  
Author(s):  
Tomás Caraballo ◽  
Adel Settati ◽  
Mohamed El Fatini ◽  
Aadil Lahrouz ◽  
Abdelouahid Imlahi
Keyword(s):  
Global Stability ◽  
Lévy Noise ◽  
Sis Model ◽  
Positive Recurrence ◽  
Noise Perturbation ◽  
Levy Noise ◽  
Stochastic Sis Model

EPIDEMIC SPREADING AND GLOBAL STABILITY OF A NEW SIS MODEL WITH DELAY ON HETEROGENEOUS NETWORKS

2015 ◽  
Vol 23 (04) ◽  
pp. 1550029 ◽  
Author(s):  
HUIYAN KANG ◽  
YIJUN LOU ◽  
GUANRONG CHEN ◽  
SEN CHU ◽  
XINCHU FU
Keyword(s):  
Global Stability ◽  
Heterogeneous Networks ◽  
Lyapunov Functional ◽  
Functional Differential Equations ◽  
Epidemic Spreading ◽  
Epidemic Threshold ◽  
Sis Model ◽  
Vector Population ◽  
Functional Differential ◽  
Disease Free

In this paper, we study a susceptible-infected-susceptible (SIS) model with time delay on complex heterogeneous networks. Here, the delay describes the incubation period in the vector population. We calculate the epidemic threshold by using a Lyapunov functional and some analytical methods, and find that adding delay increases the epidemic threshold. Then, we prove the global stability of disease-free and endemic equilibria by using the theory of functional differential equations. Furthermore, we show numerically that the epidemic threshold of the new model may change along with other factors, such as the infectivity function, the heterogeneity of the network, and the degrees of nodes. Finally, we find numerically that the delay can affect the convergence speed at which the disease reaches equilibria.

scholarly journals A non-standard discretized SIS model of epidemics

2021 ◽  
Vol 19 (1) ◽  
pp. 115-133
Author(s):  
Marcin Choiński ◽  
◽  
Mariusz Bodzioch ◽  
Urszula Foryś ◽  
◽  
...  
Keyword(s):  
Global Stability ◽  
Stationary State ◽  
Continuous System ◽  
Continuous Model ◽  
Free State ◽  
Discrete Version ◽  
Step Size ◽  
Sis Model ◽  
Homogeneous Population ◽  
Disease Free

<abstract><p>In this paper we introduce and analyze a non-standard discretized SIS epidemic model for a homogeneous population. The presented model is a discrete version of the continuous model known from literature and used by us for building a model for a heterogeneous population. Firstly, we discuss basic properties of the discrete system. In particular, boundedness of variables and positivity of solutions of the system are investigated. Then we focus on stability of stationary states. Results for the disease-free stationary state are depicted with the use of a basic reproduction number computed for the system. For this state we also manage to prove its global stability for a given condition. It transpires that the behavior of the disease-free state is the same as its behavior in the analogous continuous system. In case of the endemic stationary state, however, the results are presented with respect to a step size of discretization. Local stability of this state is guaranteed for a sufficiently small critical value of the step size. We also conduct numerical simulations confirming theoretical results about boundedness of variables and global stability of the disease-free state of the analyzed system. Furthermore, the simulations ascertain a possibility of appearance of Neimark-Sacker bifurcation for the endemic state. As a bifurcation parameter the step size of discretization is chosen. The simulations suggest the appearance of a supercritical bifurcation.</p></abstract>

Sign in / Sign up

Export Citation Format

Share Document