Transmission dynamics, global stability and control strategies of a modified SIS epidemic model on complex networks with an infective medium

In this paper, a new SIS (susceptible–infected–susceptible) epidemic model on complex networks with an infective medium is proposed. The infection rate is modified by applying the theory of probability. By using mean-field approximation, iterative analysis method and mathematical analysis, the epidemic threshold, stabilities of the disease-free equilibrium and the endemic equilibrium are studied. Moreover, some disease control strategies are proposed. The results show that the epidemic threshold plays an important role in the spread of disease. Finally, the theoretical results are confirmed by some simple numerical examples.