  This paper studies the dynamics of a network-based SIRS epidemic model with
vaccination and a nonmonotone incidence rate. This type of nonlinear incidence
can be used to describe the psychological or inhibitory effect from the
behavioral change of the susceptible individuals when the number of infective
individuals on heterogeneous networks is getting larger. Using the analytical
method, epidemic threshold $R_0$ is obtained. When $R_0$ is less than one, we
prove the disease-free equilibrium is globally asymptotically stable and the
disease dies out, while $R_0$ is greater than one, there exists a unique
endemic equilibrium. By constructing a suitable Lyapunov function, we also
prove the endemic equilibrium is globally asymptotically stable if the
inhibitory factor $\alpha$ is sufficiently large. Numerical experiments are
also given to support the theoretical results. It is shown both theoretically
and numerically a larger $\alpha$ can accelerate the extinction of the disease
and reduce the level of disease.
