Global attractivity of a network-based epidemic SIS model with nonlinear infectivity

In this paper, a new epidemic SIS model with nonlinear infectivity, as well as birth and death of nodes and edges, is investigated on heterogeneous networks. The global behavior of the model is studied mathematically. When the basic reproductive number is less than or equal to unity, it is verified that the disease dies out; otherwise, the model solutions lead to positive steady states. This paper provides a concise mathematical analysis to verify the global dynamics of the model.

► A new epidemic model with nonlinear infectivity, nonuniform connectivity, as well as birth and death, is proposed.
► The influences of model parameters and contact patterns on the disease evolution are investigated.
► A concise approach to prove the global attractivity of network models is provided.