Rumor
A rumor (American English), or rumour (British English; see spelling differences; derived from Latin:rumorem - noise), is "a tall tale of explanations of events circulating from person to person and pertaining to an object, event, or issue in p ...
is an important form of social
communication
Communication (from la, communicare, meaning "to share" or "to be in relation with") is usually defined as the transmission of information. The term may also refer to the message communicated through such transmissions or the field of inquir ...
s, and the spread of rumors plays a significant role in a variety of human affairs. There are two approaches to investigate the rumor spreading process: the microscopic models and the macroscopic models.
The macroscopic models propose a macro view about this process are mainly based on the widely used Daley-Kendall and Maki-Thompson models. Particularly, we can view rumor spread as a
stochastic process
In probability theory and related fields, a stochastic () or random process is a mathematical object usually defined as a family of random variables. Stochastic processes are widely used as mathematical models of systems and phenomena that appea ...
in social networks.
While the microscopic models are more interested more on the micro interactions between individuals.
Rumor propagation Models
In the last few years, there has been a growing interest in rumor propagation in Online social networks problems where different approaches have been proposed to investigate it.
By carefully scrutinizing the existing literature, we categorize the works into macroscopic and microscopic approaches.
Macroscopic models
The first category is mainly based on the Epidemic models
[Daley, D.J., and Kendal, D.G. 1965 Stochastic rumors, J. Inst. Maths Applics 1, p. 42.] where the pioneering research engaging rumor propagation under these models started during the 1960s.
Epidemic models
A standard model of rumor spreading was introduced by Daley and Kendall,
[. Assume there are N people in total. And those people in the network are categorized into three groups: ignorants, spreaders and stiflers, which are denoted as S, I, and R respectively hereinafter:
*I: people who are ignorant of the rumor;
*S: people who actively spread the rumor;
*R: people who have heard the rumor, but no longer are interested in spreading it.
The rumor is propagated through the population by pair-wise contacts between spreaders and others in the population. Any spreader involved in a pair-wise meeting attempts to “infect” the other individual with the rumor. In the case this other individual is an ignorant, he or she becomes a spreader. In the other two cases, either one or both of those involved in the meeting learn that the rumor is known and decided not to tell the rumor anymore, thereby turning into stiflers.
One variant is the Maki-Thompson model. In this model, rumor is spread by directed contacts of the spreaders with others in the population. Furthermore, when a spreader contacts another spreader only the initiating spreader becomes a stifler. Therefore, three types of interactions can happen with certain rates.
::which says when a spreader meet an ignorant, the ignorant will become a spreader.
::which says when two spreaders meet with each other, one of them will become a stifler.
::which says when a spreader meet a stifler, the spreader will lose the interest in spreading the rumor, so become a stifler.
Of course we always have conservation of individuals:]
:
The change in each class in a small time interval is:
:
: