A general class of spreading processes with non-Markovian dynamics

TL;DR

This paper introduces the SI*V* model, a highly flexible framework for modeling complex spreading processes with non-Markovian dynamics on arbitrary networks, encompassing many existing models and enabling more realistic simulations.

Contribution

The paper presents the SI*V* model, a general and adaptable framework that captures non-Markovian spreading processes and unifies numerous existing compartmental models.

Findings

The SI*V* model generalizes many classical epidemiological models.

Conditions for stability of the disease-free equilibrium are derived.

Simulations demonstrate the model's ability to capture complex dynamics.

Abstract

In this paper we propose a general class of models for spreading processes we call the $SI^*V^*$ 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 $SI^*V^*$ 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.