Abstract
Many contagions spread over various types of communication networks and their spreading dynamics have been extensively studied in the literature. Here we propose a general model for the concurrent spread of an arbitrary number of contagions in complex networks. The model is stochastic and runs in discrete time, and includes two widely used mechanisms by which a node can change its state. The first, termed the spontaneous state change mechanism, describes spontaneous transition to another state, while the second, termed the contact-induced state change mechanism, describes acquiring other contagions due to contact with the neighbors. We consider reactive discrete-time spreading processes of multiple concurrent contagions where time steps are of finite size without neglecting the possibility of multiple infecting events in a single time step. An essential element for making the model numerically tractable is the use of an approximation for the probability that a node transits to a specific state given any set of neighboring states. Different transmission probabilities may be present between each pair of states. We also derive corresponding continuous–time equations that are simple and intuitive. The model includes many well-known epidemic and rumor spreading models as a special case and it naturally captures spreading processes in multiplex networks.
Highlights
Epidemiological models, developed as tools for analyzing the spread and control of infectious diseases, have been adapted across many scientific fields such as ecology, immunology, social science, computer science, marketing and economy
A key instrument which we use to make this general model applicable for simulations is an approximation for the exact probability that a node will adopt a specific state from its neighbors
We have proposed a general model for the spread of an arbitrary number of infections or contagions on networks, in which several contagions can simultaneously compete to infect a node
Summary
Epidemiological models, developed as tools for analyzing the spread and control of infectious diseases, have been adapted across many scientific fields such as ecology, immunology, social science, computer science, marketing and economy. They focus on modeling the dynamics of contagious entities ( called ‘‘memes’’ in the literature) as diverse as communicable diseases, cultural characteristics (such as religious beliefs, fads or innovations), addictions, or information spread (through rumors, e-mail messages, web blogs, peer-to-peer computer networks, etc) Both deterministic and stochastic epidemic models have been suggested, addressing complementary questions [1,2,3,4]. The model suggested in this paper has three main characteristics It belongs to the class of stochastic discrete-time models, applies to arbitrary graphs, and can quantify the microscopic dynamics at the individual level by computing the probability that any given node is in a given state. We will often refer to them as states as well, from the representation of the dynamics of each node as a Markov chain
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