Global Stability of Virus Spreading in Complex Heterogeneous Networks

Global stability of an SIS epidemic model with feedback mechanism on networks

“…In the famous works [2,3], PastorSatorras and Vespignani established a dynamical mean-field equation based on the SIS model and showed that the finite-size effects induce an epidemic threshold, which approaches zero at increasing sizes, so that if the effective spreading rate is above this threshold, then the infection spreads and becomes endemic. For such significant finding, until recently, a mathematically rigorous proof was given by Wang and Dai [14]. Stability analysis is an important tool to understand the spreading dynamics of epidemic models on complex networks.…”

Compartmental Disease Models with Heterogeneous Populations: A Survey

“…Specifically, we provide three methods to prove the global stability of the endemic equilibrium when R 0 > 1: the original proof by Lajmanovich and Yorke in [4], the graph-theoretic approach as shown in [25,Sec. 6], and the comparison method in [45]. We conclude with discussions and several open problems in Sect.…”

“…Besides Lyapunov function methods, other methods such as comparison arguments [45] and the theory of monotone dynamical systems [46] have also been applied to establish global dynamics for heterogeneous models. In Sect.…”

Dynamics of an SIS Model on Homogeneous Networks with Delayed Reduction of Contact Numbers

“…A great deal of research in mathematical epidemiology has been done for complex networks during the past years [1], [2], [3], [4], [5], [6], [7], [8], [9], [10], [11], [12]. These works focus mostly on two different complex networks: the Watts-Strogatz model and the Barabási-Albert model.…”