Resumen de On a Rumor Propagation Model with Spatial Heterogeneity
Mengxin Chen, Hari Mohan Srivastava
Rumors or wrong information are always spread in different spatial locations by virtue of various available media. Therefore, the propagation ability of rumors or wrong information should be different in different geographical locations. In this paper, we report the dynamical behaviors of a diffusive SI (susceptible-infected) type rumor propagation model in a spatially heterogeneous environment. In view of the fact that rumor-refuting is a common phenomenon in the real world, we introduce this concern in the rumor propagation model. We first derive the properties of uniform boundedness and permanence of the rumor propagation model. These results indicate that the rumor propagation model has at least one rumor-spreading steady state. Thereafter, the asymptotic profiles of the rumor-spreading steady state are reported. We thus find that such rumor-spreading steady state exists if one of the migration rates of the rumor-infected individuals or the rumor-susceptible individuals tends to zero and infinity, respectively. Our theoretical results reveal that this rumor propagation model can admit wealthy dynamical profiles in a spatially heterogeneous environment. Some numerical results are also presented in order to check the theoretical conclusions.
