Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Dynamic Curing and Network Design in SIS Epidemic Processes

Yuhao Yi, Liren Shan, Shijie Wang, Philip E. Paré, Karl H. Johansson

TL;DR

This work addresses fast extinction of SIS epidemics on networks by combining dynamic curing policies with network-design interventions. Building on the CURE policy framework, it develops efficient approximation algorithms for impedance and its fair variant, enabling near-optimal curing orders under budget constraints. It also formulates and solves network-design problems to reduce the total infection rate, using LP/SDP relaxations and tree-embedding techniques to guarantee performance bounds. The proposed methods yield sublinear extinction times and provide practical strategies for co-designing medical and non-pharmaceutical interventions, demonstrated through simulations on real-world networks. Overall, the study advances tractable, theory-backed tools for dynamically controlling SIS epidemics in complex networks.

Abstract

This paper studies efficient algorithms for dynamic curing policies and the corresponding network design problems to guarantee the fast extinction of epidemic spread in a susceptible-infected-susceptible (SIS) model. We consider a Markov process-based SIS epidemic model. We provide a computationally efficient curing algorithm based on the curing policy proposed by Drakopoulos, Ozdaglar, and Tsitsiklis (2014). Since the corresponding optimization problem is NP-hard, finding optimal policies is intractable for large graphs. We provide approximation guarantees on the curing budget of the proposed dynamic curing algorithm. We also present a curing algorithm fair to demographic groups. When the total infection rate is high, the original curing policy includes a waiting period in which no measure is taken to mitigate the spread until the rate slows down. To avoid the waiting period, we study network design problems to reduce the total infection rate by deleting edges or reducing the weight of edges. Then the curing processes become continuous since the total infection rate is restricted by network design. We provide algorithms with provable guarantees for the considered network design problems. In summary, the proposed curing and network design algorithms together provide an effective and computationally efficient approach that mitigates SIS epidemic spread in networks.

Dynamic Curing and Network Design in SIS Epidemic Processes

TL;DR

This work addresses fast extinction of SIS epidemics on networks by combining dynamic curing policies with network-design interventions. Building on the CURE policy framework, it develops efficient approximation algorithms for impedance and its fair variant, enabling near-optimal curing orders under budget constraints. It also formulates and solves network-design problems to reduce the total infection rate, using LP/SDP relaxations and tree-embedding techniques to guarantee performance bounds. The proposed methods yield sublinear extinction times and provide practical strategies for co-designing medical and non-pharmaceutical interventions, demonstrated through simulations on real-world networks. Overall, the study advances tractable, theory-backed tools for dynamically controlling SIS epidemics in complex networks.

Abstract

This paper studies efficient algorithms for dynamic curing policies and the corresponding network design problems to guarantee the fast extinction of epidemic spread in a susceptible-infected-susceptible (SIS) model. We consider a Markov process-based SIS epidemic model. We provide a computationally efficient curing algorithm based on the curing policy proposed by Drakopoulos, Ozdaglar, and Tsitsiklis (2014). Since the corresponding optimization problem is NP-hard, finding optimal policies is intractable for large graphs. We provide approximation guarantees on the curing budget of the proposed dynamic curing algorithm. We also present a curing algorithm fair to demographic groups. When the total infection rate is high, the original curing policy includes a waiting period in which no measure is taken to mitigate the spread until the rate slows down. To avoid the waiting period, we study network design problems to reduce the total infection rate by deleting edges or reducing the weight of edges. Then the curing processes become continuous since the total infection rate is restricted by network design. We provide algorithms with provable guarantees for the considered network design problems. In summary, the proposed curing and network design algorithms together provide an effective and computationally efficient approach that mitigates SIS epidemic spread in networks.
Paper Structure (21 sections, 13 theorems, 32 equations, 3 figures)

This paper contains 21 sections, 13 theorems, 32 equations, 3 figures.

Table of Contents

  1. Introduction
  2. Contributions
  3. Outline
  4. Preliminaries
  5. Concepts and Notations
  6. Epidemic Model
  7. Problem Formulations
  8. Curing Policies
  9. Network Design
  10. Curing Algorithms
  11. Algorithm for CURE Policy
  12. Fair Curing Algorithms
  13. Network Design
  14. Network Design for Curing Policies
  15. Network Design for Minimizing the Maximum Restricted Cut
  16. ...and 6 more sections

Key Result

Theorem 1

Given a graph $G$, suppose the curing budget $r \geq \max\{\alpha \mathcal{W} \log^2 n, 8d_{max} \log n\}$, where $\mathcal{W}$ is the cutwidth of graph $G$ and $\alpha$ is a fixed constant. Then, there exists a polynomial-time curing algorithm such that the expected extinction time is at most $O(n\

Figures (3)

  • Figure 1: Comparison of CURE (using Algorithm \ref{['alg:apprImpe']}) with baseline policies
  • Figure 2: Comparison of network design algorithms: 1) CURE without network design; 2) CURE with linear programming network design; 3) Random curing rate allocation with SDP.
  • Figure 3: The construction of a good partition in $S'$. The top figure corresponds to the optimal $\gamma$-fair crusade. The bottom figure corresponds to a good partition.

Theorems & Definitions (31)

  • Definition 1
  • Definition 2
  • Definition 3
  • Definition 4
  • Definition 5
  • Definition 6
  • Theorem 1
  • Lemma 1: Section 3.3 in LR99
  • Theorem 2
  • proof
  • ...and 21 more