29 research outputs found
A general class of spreading processes with non-Markovian dynamics
In this paper we propose a general class of models for spreading processes we
call the model. Unlike many works that consider a fixed number of
compartmental states, we allow an arbitrary number of states on arbitrary
graphs with heterogeneous parameters for all nodes and edges. As a result, this
generalizes an extremely large number of models studied in the literature
including the MSEIV, MSEIR, MSEIS, SEIV, SEIR, SEIS, SIV, SIRS, SIR, and SIS
models. Furthermore, we show how the model allows us to model
non-Poisson spreading processes letting us capture much more complicated
dynamics than existing works such as information spreading through social
networks or the delayed incubation period of a disease like Ebola. This is in
contrast to the overwhelming majority of works in the literature that only
consider spreading processes that can be captured by a Markov process. After
developing the stochastic model, we analyze its deterministic mean-field
approximation and provide conditions for when the disease-free equilibrium is
stable. Simulations illustrate our results