Stability of the SNIS epidemic spreading model with contagious incubation period over heterogeneous networks

Abstract In this paper, a novel susceptible–infected–susceptible epidemic model with contagious incubation period is proposed by using the N-intertwined mean field approximation on directed and heterogeneous networks. Both continuous and impulsive strategies that consider the detection and identification of individuals in incubation period are studied. The impacts of the incubation period incorporating with the network topology and the effects of the strategies on the epidemic spreading process are discussed. We analyze the stability of disease-free equilibrium and obtain the corresponding sufficient conditions by means of Lyapunov–Razumikhin functions and inequality techniques. Numerical simulations are presented to illustrate and validate the theoretical analysis. These results provide some meaningful clues for the public health department to conduct appropriate and effective defensive measures to eradicate the epidemic in the crowd.

[1]  Ming Tang,et al.  Suppressing epidemic spreading in multiplex networks with social-support , 2017, 1708.02507.

[2]  Ping Hu,et al.  Individual-based optimal weight adaptation for heterogeneous epidemic spreading networks , 2018, Commun. Nonlinear Sci. Numer. Simul..

[3]  Tianshou Zhou,et al.  The influence of time delay on epidemic spreading under limited resources , 2018, Physica A: Statistical Mechanics and its Applications.

[4]  Ba Di Ya,et al.  Matrix Analysis , 2011 .

[5]  Yaohui Pan,et al.  The impact of multiple information on coupled awareness-epidemic dynamics in multiplex networks , 2018 .

[6]  Sanyang Liu,et al.  Bifurcation of a heroin model with nonlinear incidence rate , 2017 .

[7]  P E Sartwell,et al.  The incubation period and the dynamics of infectious disease. , 1966, American journal of epidemiology.

[8]  Zhen Wang,et al.  Suppressing epidemic spreading by risk-averse migration in dynamical networks , 2018, 1802.01250.

[9]  Ping Hu,et al.  Epidemic spreading on random surfer networks with optimal interaction radius , 2018, Commun. Nonlinear Sci. Numer. Simul..

[10]  Lu-Xing Yang,et al.  The impact of nonlinear infection rate on the spread of computer virus , 2015 .

[11]  W. O. Kermack,et al.  A contribution to the mathematical theory of epidemics , 1927 .

[12]  Zhongjun Ma,et al.  Dynamic stability of an SIQS epidemic network and its optimal control , 2019, Commun. Nonlinear Sci. Numer. Simul..

[13]  Jianhua Shen,et al.  Impulsive stabilization of functional differential equations by Lyapunov-Razumikhin functions , 1999 .

[14]  P. Van Mieghem,et al.  Susceptible-infected-susceptible epidemics on the complete graph and the star graph: exact analysis. , 2013, Physical review. E, Statistical, nonlinear, and soft matter physics.

[15]  Hai-Feng Zhang,et al.  Effects of awareness diffusion and self-initiated awareness behavior on epidemic spreading - An approach based on multiplex networks , 2015, Communications in Nonlinear Science and Numerical Simulation.

[16]  Yuan Yuan,et al.  A time-delayed epidemic model for Ebola disease transmission , 2016, Appl. Math. Comput..

[17]  Jinhu Xu,et al.  Global stability of a multi‐group model with distributed delay and vaccination , 2017 .

[18]  Huiyan Kang,et al.  Spreading Dynamics of an SEIR Model with Delay on Scale-Free Networks , 2020, IEEE Transactions on Network Science and Engineering.

[19]  Tao Yang,et al.  Impulsive control , 1999, IEEE Trans. Autom. Control..

[20]  Zizhen Zhang,et al.  Qualitative analysis for a delayed epidemic model with latent and breaking-out over the Internet , 2017 .

[21]  Asier Ibeas,et al.  On the stability of an SEIR epidemic model with distributed time-delay and a general class of feedback vaccination rules , 2015, Appl. Math. Comput..

[22]  Yan Zhang,et al.  A remark on stationary distribution of a stochastic SIR epidemic model with double saturated rates , 2018, Appl. Math. Lett..

[23]  Ming Tang,et al.  Suppression of epidemic spreading in complex networks by local information based behavioral responses , 2014, Chaos.

[24]  Zhi-Hong Guan,et al.  An epidemic spreading model on adaptive scale-free networks with feedback mechanism , 2016 .

[25]  Chenquan Gan,et al.  Modeling and analysis of the effect of network eigenvalue on viral spread , 2016 .

[26]  Qingchu Wu,et al.  Dynamical behavior of susceptible-infected-recovered-susceptible epidemic model on weighted networks , 2018 .