# Optimal Vaccine Allocation to Control Epidemic Outbreaks in Arbitrary Networks

arXiv: https://arxiv.org/abs/1303.3984 · HTML: https://mlsanity.com/paper/1303.3984/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 16 Mar 2013.

## Built on by (most cited first, 3 of 3)

- [Controlling Epidemic Spread using Probabilistic Diffusion Models on Networks](https://mlsanity.com/paper/2202.08296/) (2022)
- [Uncertainty Informed Optimal Resource Allocation with Gaussian Process based Bayesian Inference](https://mlsanity.com/paper/2307.00032/) (2023)
- [Spread Control Method on Unknown Networks Based on Hierarchical Reinforcement Learning](https://mlsanity.com/paper/2308.14311/) (2023)

## Abstract (arXiv)

We consider the problem of controlling the propagation of an epidemic outbreak in an arbitrary contact network by distributing vaccination resources throughout the network. We analyze a networked version of the Susceptible-Infected-Susceptible (SIS) epidemic model when individuals in the network present different levels of susceptibility to the epidemic. In this context, controlling the spread of an epidemic outbreak can be written as a spectral condition involving the eigenvalues of a matrix that depends on the network structure and the parameters of the model. We study the problem of finding the optimal distribution of vaccines throughout the network to control the spread of an epidemic outbreak. We propose a convex framework to find cost-optimal distribution of vaccination resources when different levels of vaccination are allowed. We also propose a greedy approach with quality guarantees for the case of all-or-nothing vaccination. We illustrate our approaches with numerical simulations in a real social network.