Epidemic spreading and global stability of an SIS model with an infective vector on complex networks

2015 ◽  
Vol 27 (1-3) ◽  
pp. 30-39 ◽  
Author(s):  
Huiyan Kang ◽  
Xinchu Fu
Keyword(s):  
Complex Networks ◽  
Global Stability ◽  
Epidemic Spreading ◽  
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.

THE SIS MODEL WITH TIME DELAY ON COMPLEX NETWORKS

2009 ◽  
Vol 19 (02) ◽  
pp. 623-628 ◽  
Author(s):  
XIN-JIAN XU ◽  
GUANRONG CHEN
Keyword(s):  
Complex Networks ◽  
Delay Time ◽  
Transmission Rate ◽  
Small World ◽  
Small World Networks ◽  
Epidemic Spreading ◽  
Epidemic Threshold ◽  
Exponential Form ◽  
Sis Model ◽  
Scale Free

We present a time-delayed SIS model on complex networks to study epidemic spreading. We found that the existence of delay will affect, and oftentimes enhance, both outbreak and prevalence of infectious diseases in the networks. For small-world networks, we found that the epidemic threshold and the delay time have a power-law relation. For scale-free networks, we found that for a given transmission rate, the epidemic prevalence has an exponential form, which can be analytically obtained, and it decays as the delay time increases. We confirm all results by sufficient numerical simulations.

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

scholarly journals GEOGRAPHICAL EFFECTS ON EPIDEMIC SPREADING IN SCALE-FREE NETWORKS

2006 ◽  
Vol 17 (12) ◽  
pp. 1815-1822 ◽  
Author(s):  
XIN-JIAN XU ◽  
WEN-XU WANG ◽  
TAO ZHOU ◽  
GUANRONG CHEN
Keyword(s):  
Metric Space ◽  
Healthy Individual ◽  
Euclidean Distance ◽  
Nearest Neighbors ◽  
Epidemic Spreading ◽  
Sis Model ◽  
Scale Free ◽  
Scale Free Networks ◽  
Disease Spreading

Many real networks are embedded in a metric space: the interactions among individuals depend on their spatial distances and usually take place among their nearest neighbors. In this paper, we introduce a modified susceptible-infected-susceptible (SIS) model to study geographical effects on the spread of diseases by assuming that the probability of a healthy individual infected by an infectious one is inversely proportional to the Euclidean distance between them. It is found that geography plays a more important role than hubs in disease spreading: the more geographically constrained the network is, the more highly the epidemic prevails.

scholarly journals Control of epidemic spreading on complex networks by local traffic dynamics

2011 ◽  
Vol 84 (4) ◽  
Author(s):  
Han-Xin Yang ◽  
Wen-Xu Wang ◽  
Ying-Cheng Lai ◽  
Yan-Bo Xie ◽  
Bing-Hong Wang
Keyword(s):  
Complex Networks ◽  
Epidemic Spreading ◽  
Traffic Dynamics
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