# Analysis of Exact and Approximated Epidemic Models over Complex Networks

@article{Azizan2016AnalysisOE, title={Analysis of Exact and Approximated Epidemic Models over Complex Networks}, author={Navid Azizan and Hyoung Jun Ahn and Babak Hassibi}, journal={ArXiv}, year={2016}, volume={abs/1609.09565} }

We study the spread of discrete-time epidemics over arbitrary networks for well-known propagation models, namely SIS (susceptible-infected-susceptible), SIR (susceptible-infected-recovered), SIRS (susceptible-infected-recovered-susceptible) and SIV (susceptible-infected-vaccinated). Such epidemics are described by $2^n$- or $3^n$-state Markov chains. Ostensibly, because analyzing such Markov chains is too complicated, their $O(n)$-dimensional nonlinear "mean-field" approximation, and its…

## 11 Citations

### Improved bounds on the epidemic threshold of exact SIS models on complex networks

- Computer Science, Mathematics2016 IEEE 55th Conference on Decision and Control (CDC)
- 2016

Improved upper bounds on the exact marginal probabilities of infection are provided, by also taking pairwise infection probabilities into account, and tighter eigenvalue conditions that guarantee fast mixing of the Markov chain are derived.

### Inferring Epidemic Parameters in Networked SIS Epidemics

- Mathematics
- 2017

The mathematical modeling and analysis of epidemic spread is of great importance in understating how epidemics behave and and how to control them, and it has attracted significant interest from…

### Transient Dynamics of Epidemic Spreading and Its Mitigation on Large Networks

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- 2019

A theoretical framework is developed that allows for an accurate closed-form approximate solution to the original SI dynamics on any arbitrary network, which captures the temporal dynamics over all time and is tighter than the existing approximation, and also to provide a new interpretation via reliability theory.

### Prophylaxis of Epidemic Spreading with Transient Dynamics

- EconomicsArXiv
- 2020

The results show that individual behaviours can be extremely inefficient in the face of epidemic propagation but that policy can take advantage of the network structure to design efficient containment policies.

### Game-Theoretic Protection Against Networked SIS Epidemics by Human Decision-Makers

- EconomicsIFAC-PapersOnLine
- 2019

### Initialization and Curing Policies for Polya Contagion Networks

- Computer ScienceSIAM J. Control. Optim.
- 2022

This paper investigates optimization policies for resource distribution in network epidemics using a model that derives from the classical Polya process, and introduces heuristic policies that primarily function on the basis of limiting the number of targeted nodes within a particular network setup.

### Networked Infectious Disease–Contaminated Water Model

- Economics2019 18th European Control Conference (ECC)
- 2019

A continuous-time virus spreading model that includes a human-contact network and a water component that may be contaminated that captures the behavior of Dr. John Snow's pioneering cholera dataset is proposed.

### Manifold Optimization Over the Set of Doubly Stochastic Matrices: A Second-Order Geometry

- Computer Science, MathematicsIEEE Transactions on Signal Processing
- 2019

This paper suggests using a Riemannian optimization approach to solve a subset of convex optimization problems wherein the optimization variable is a doubly stochastic matrix and reveals that the proposed framework outperforms conventional generic and specialized approaches, especially in high dimensions.

### Mitigating Time-Constrained Stolen-Credentials Content Poisoning in an NDN Setting

- Computer Science2019 29th International Telecommunication Networks and Applications Conference (ITNAC)
- 2019

It is argued that limited-time validity of stolen credentials gives rise to a mitigation scheme that does not require costly object examination, and instead, propagation of trust in an object is carefully designed.

### Scalable Reinforcement Learning for Multiagent Networked Systems

- Computer ScienceOperations Research
- 2022

This article designs a scalable RL method, named scalable actor critic (SAC), for large networked systems and exploits the network structure to derive an exponential decay property, which enables the design of the SAC approach.

## References

SHOWING 1-10 OF 34 REFERENCES

### SIRS epidemics on complex networks: Concurrence of exact Markov chain and approximated models

- Mathematics2015 54th IEEE Conference on Decision and Control (CDC)
- 2015

It is shown that under the specific threshold where the disease-free state is a globally stable fixed point of both the linear and nonlinear models, the exact underlying Markov chain has an O(log n) mixing time, which means the epidemic dies out quickly.

### Improved bounds on the epidemic threshold of exact SIS models on complex networks

- Computer Science, Mathematics2016 IEEE 55th Conference on Decision and Control (CDC)
- 2016

Improved upper bounds on the exact marginal probabilities of infection are provided, by also taking pairwise infection probabilities into account, and tighter eigenvalue conditions that guarantee fast mixing of the Markov chain are derived.

### Stability of epidemic models over directed graphs: A positive systems approach

- MathematicsAutom.
- 2016

### Stability analysis of generalized epidemic models over directed networks

- Mathematics53rd IEEE Conference on Decision and Control
- 2014

A generalized version of the Susceptible-Exposed-Infected-Vigilant (SEIV) disease spreading model over arbitrary directed graphs that captures the fact that infected individuals may act differently when they are aware of their infection.

### Discrete-time Markov chain approach to contact-based disease spreading in complex networks

- Mathematics
- 2010

Many epidemic processes in networks spread by stochastic contacts among their connected vertices. There are two limiting cases widely analyzed in the physics literature, the so-called contact process…

### On the mixing time of the SIS Markov chain model for epidemic spread

- Mathematics, Computer Science53rd IEEE Conference on Decision and Control
- 2014

This paper study the relationship between the Markov chain model and n-dimensional nonlinear dynamical system which approximates the evolution of the marginal probability that each node is infected, and shows that this approximated model gives an upper bound on the true marginal probability as given by the MarkOV chain model.

### Analysis of epidemic spreading of an SIRS model in complex heterogeneous networks

- MathematicsCommun. Nonlinear Sci. Numer. Simul.
- 2014

### An upper bound for the epidemic threshold in exact Markovian SIR and SIS epidemics on networks

- Mathematics53rd IEEE Conference on Decision and Control
- 2014

From a new Laplacian expression, the exact governing equations for both the SIR and SIS epidemic models on networks are presented and a general upper bound for the epidemic SIS threshold in any graph is deduced.

### Global dynamics of epidemic spread over complex networks

- Mathematics52nd IEEE Conference on Decision and Control
- 2013

Conditions under which the second fixed point attracts all non-origin points are given and it is shown that for random Erdös-Rényi graphs this happens with high probability.

### The Cost of an Epidemic over a Complex Network: A Random Matrix Approach

- MathematicsArXiv
- 2013

This work calculates the total economic impact of an epidemic over a complex network using tools from random matrix theory, accounting for both the immunization and disease costs for various immunization strategies and determining the optimal immunization.