Epidemics on contact networks: a general stochastic approach

TL;DR

This paper introduces a versatile stochastic framework for modeling epidemic dynamics on contact networks, enabling comparison of complex models and efficient simulations of spreading processes.

Contribution

It presents a general systematic approach based on Markov processes that can unify and compare existing epidemic models and improve simulation efficiency.

Findings

Applicable to SIS and SIR epidemic models

Achieves accurate results with low computational cost

Provides a common framework for complex epidemic models

Abstract

Dynamics on networks is considered from the perspective of Markov stochastic processes. We partially describe the state of the system through network motifs and infer any missing data using the available information. This versatile approach is especially well adapted for modelling spreading processes and/or population dynamics. In particular, the generality of our systematic framework and the fact that its assumptions are explicitly stated suggests that it could be used as a common ground for comparing existing epidemics models too complex for direct comparison, such as agent-based computer simulations. We provide many examples for the special cases of susceptible-infectious-susceptible (SIS) and susceptible-infectious-removed (SIR) dynamics (e.g., epidemics propagation) and we observe multiple situations where accurate results may be obtained at low computational cost. Our perspective reveals a subtle balance between the complex requirements of a realistic model and its basic assumptions.