The main thrust of this study is to investigate the Dynamical model for the spread of rumors. In today’s anxiety-laden security environment, rumors can provide unique insights into the current grievances and fears of a given population; they can also act as powerful agents of influence. For example, by propagating rumors about civilian abuses at the hands of the government or military, an adversary can foster a sense of uncertainty and sow distrust between a government and its population. Conversely, by evaluating and understanding rumors currently circulating through a population, a government or military force can overcome obstacles to its programs, and can provide targeted messages of reassurance to the populace when necessary. Nowadays, with the emergence of the internet, rumors can be spread by instant messengers, emails, or publishing. With this new pattern of spreading, an ISRW dynamical model considering the medium as a subclass is established. Beside the dynamical analysis of the model, we mainly explore the mechanism of spreading of individuals-to-individuals and medium-to-individual. By numerical simulation, we find that if we want to control the rumor spreading, it will not only need to control the rate of change of the spreader subclass, but also need to control the change of the information about rumor in medium which has larger influence. Moreover, to control the effusion of rumor is more important than deleting existing information about rumor. On the one hand, government should enhance the management of internet. On the other hand, relevant legal institutions for punishing the rumor creator and spreader on internet who can be tracked should be established. Using this way, involved authorities can propose efficient measures to control the rumor spreading to keep the stabilization of society and development of economy.
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