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

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. • An SNIS model considering the contagious incubation period is established. • Two intervention strategies for suppressing epidemic are proposed. • The impact of the incubation period and network topology is investigated. • Sufficient conditions for virus-free equilibrium stability are obtained. [ABSTRACT FROM AUTHOR]