d="para0001">A spatial-temporal rumor propagation model with discrete and non-local delays is regarded.
dd><dt class="label">•dt><dd>d="para0002">Stability and Hopf bifurcation are proved in a strict mathematical way.
dd><dt class="label">•dt><dd>d="para0003">Sensitivity analysis is applied to search active parameters.
dd><dt class="label">•dt><dd>d="para0004">Hopf bifurcation causes an oscillation phenomenon in this model.
dd><dt class="label">•dt><dd>d="para0005">Numerical simulations provide a new insight into rumor spreading in online social networks.
dd>dl>