Optimal control of a rumor propagation model in online social network by considering influential nodes

Social networking platforms give people an opportunity to get in contact with each other irrespective of boundaries. Through these platforms, any individual can easily follow the ideas of other individuals like friends, relatives, politicians, actors, etc, and get in contact with them. In this paper, we examine rumor propagation with two types of infected people: highly influential people and ordinary people. Some ordinary people, blindly follow the messages shared by highly influential people. By using this concept we analyze the rumor-spreading model in networks (homogeneous and heterogeneous). We applied control strategies in homogeneous networks and observed that government policies to control rumor propagation can reduce its spread. Immunization in heterogeneous networks by giving proper information and education to people about facts can also reduce the spread and help people make the right decision when they come across a rumor