To study rumor spreading, a novel rumor spreading model with latent, constant recruitment, and varying total population is investigated. We carry out a global qualitative analysis of the rumor spreading model with latent, constant recruitment, and varying total population and studied the existence and stability of the rumor-elimination and prevailing equilibria and the impact different management strategies have on the rumor spreading process. The Runge-Kutta method is used for numerical simulation, and the simulation results imply that increasing the efforts to crack down on rumor spreaders, the timely disclosure of transparent information, the popularization of scientific knowledge, and the improvement of the ignorants’ discrimination may be effective rumor control measures. 1. Introduction Rumor is a typical social phenomenon that runs through the whole evolutionary history of mankind, and its spreading plays a significant role in a variety of human affairs [1–4]. A rumor is “an unverified account or explanation of events circulating from person to person and pertaining to an object, event, or issue in public concern” [2]. Rumor is usually created to defame someone or to spread false information about public events; it not only infringes upon others’ interests, but also poses a threat to social stability, and it appears when a group tries to make sense of an ambiguous, uncertain, or chaotic situation. For example, in 2011, the Fukushima Daiichi nuclear disaster resulted from a 9.0-magnitude earthquake and ensuing tsunami in Japan caused a salt-buying frenzy in China. This salt-buying frenzy came from the rumors that Japan’s nuclear leak would contaminate the sea off east China’s Shandong province, thereby compromising the future safety of salt taken from the sea, and additionally it is believed that iodized salt helps protect people from nuclear radiation or the salt produced from contaminated seawater will be unsafe to eat. With the rumors spreading, this frenzy swept across China and caused social panic as well as instability in just a few days. From the afternoon of March 16, 2011, people in coastal areas such as Zhejiang, Jiangsu, and Shanghai, rushed out to buy up supplies, pushing up the price tenfold, before the panic spread inland. The next day, other inland areas such as Shanxi, Hubei, Anhui, Jiangxi, Guizhou, and Sichuan provinces were also caught up in the panic buying. The situation eased after the government ordered the securing of salt supplies and as experts confirmed that salt was almost useless to counter radiation. Other rumors have
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