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

Abstract

We study the global stability of endemic equilibrium of an SIS epidemic model with feedback mechanism on networks. The model was proposed by J. Zhang and J. Sun (Physica A 394:24-32, 2014), who obtained the local asymptotic stability of endemic equilibrium. Our main purpose is to show that if the feedback parameter is sufficiently large or if the basic reproductive number belongs to the interval (1, 2], then the endemic equilibrium is globally asymptotically stable. We also present numerical simulations to illustrate the theoretical results.

The bifurcation analysis and optimal feedback mechanism for an SIS epidemic model on networks

“…In Theorem 2.1, Remark 2.1, and Remark 2.2, we pay attention to the critical case R 0 = 1 and present the strict theoretical proof for the existence of the transcritical bifurcation. Thus, the above results improve and supplement the corresponding results in [7] and [29,30].…”

“…In detail, those individuals with small degree should be strengthened on the BA network and the control strength is more balanced for the nodes with different degree on the WS network. All the results in this paper are a good extension and supplement to those in [7,29], and [30]. The above analysis will have certain guidance when analyzing and controlling the disease spread.…”

“…So most of the nodes should be strengthened. The main results in this paper are a good extension and supplement to those in [7,29], and [30]. All the above simulation analysis may provide the public some guidance when the whole society faces up to infectious diseases.…”

“…In [29], a modified SIS network model with infective medium and feedback mechanism was presented. In [30], the authors obtained that the endemic equilibrium is globally asymptotically stable if the feedback parameter is sufficiently large or if the basic reproductive number belongs to a special interval. We notice that the feedback mechanism in [7,29], and [30] is reflected by introducing a constant coefficient.…”

“…In [30], the authors obtained that the endemic equilibrium is globally asymptotically stable if the feedback parameter is sufficiently large or if the basic reproductive number belongs to a special interval. We notice that the feedback mechanism in [7,29], and [30] is reflected by introducing a constant coefficient. However, we think that the initiative response of people is constantly changing and it is more reasonable to introduce the time-varying feedback parameter.…”