PDE limits of stochastic SIS epidemics on networks

  title={PDE limits of stochastic SIS epidemics on networks},
  author={Frances Di Lauro and J. Croix and L. Berthouze and I. Kiss},
  journal={arXiv: Populations and Evolution},
Stochastic epidemic models on networks are inherently high-dimensional and the resulting exact models are intractable numerically even for modest network sizes. Mean-field models provide an alternative but can only capture average quantities, thus offering little or no information about variability in the outcome of the exact process. In this paper we conjecture and numerically prove that it is possible to construct PDE-limits of the exact stochastic SIS epidemics on regular and Erdős-Renyi… Expand

Figures and Tables from this paper


Approximate master equations for dynamical processes on graphs
We extrapolate from the exact master equations of epidemic dynamics on fully connected graphs to non-fully connected by keeping the size of the state space N + 1, where N is the number of nodes inExpand
Network inference from population-level observation of epidemics
This work uses extensive simulations over Regular, Erdős–Rényi and Barabási–Albert networks to build network class-specific priors and uses Bayesian model selection to recover the most likely underlying network class, based only on a single realisation of the epidemic. Expand
Inferring network properties based on the epidemic prevalence
It is found that some of the network metrics, namely those that are sensitive to the epidemic prevalence, can be roughly inferred if the network type is known, and a simulated annealing link-rewiring algorithm is proposed to obtain an optimized network whose prevalence is close to the benchmark. Expand
Mathematics of Epidemics on Networks: From Exact to Approximate Models
This textbook provides an exciting new addition to the area of network science featuring a stronger and more methodical link of models to their mathematical origin and explains how these relate toExpand
A Stochastic Differential Equation SIS Epidemic Model
It is proved that this classical susceptible-infected-susceptible epidemic model is formulated as a stochastic differential equation (SDE) for the number of infectious individuals and that this SDE has a unique global positive solution. Expand
Law of large numbers for the SIR epidemic on a random graph with given degrees
The main result is that, conditional on a large outbreak, the evolutions of certain quantities of interest, such as the fraction of infective vertices, converge to deterministic functions of time. Expand
Effective degree network disease models
The threshold parameter for the SIS model is shown to be larger than that derived from percolation theory for a model with the same disease and network parameters, and consequently a disease may be able to invade with lower transmission than predicted by percolated theory. Expand
Epidemic processes in complex networks
A coherent and comprehensive review of the vast research activity concerning epidemic processes is presented, detailing the successful theoretical approaches as well as making their limits and assumptions clear. Expand
Large graph limit for an SIR process in random network with heterogeneous connectivity
We consider an SIR epidemic model propagating on a Configuration Model network, where the degree distribution of the vertices is given and where the edges are randomly matched. The evolution of theExpand
Quasi-stationary distributions and population processes
This survey concerns the study of quasi-stationary distributions with a specific focus on models derived from ecology and population dynamics. We are concerned with the long time behavior ofExpand