Three-layer model for the control of epidemic infection over multiple social networks

Abstract

Abstract This paper presents a hierarchical approach for controlling the spread of an epidemic disease. The approach consists of a three-layer architecture where a set of two-layer multiple social networks is governed by a (third) top-layer consisting of an optimal control policy. Each of the two-layer social networks is modeled by a microscopic Markov chain. On top of all the two-layer networks is an optimal control policy that has been developed by using an underlying Markov Decision Process (MDP) model. Mathematical models pertaining to the top-level MDP as well as two-layer microscopic Markov chains have been presented. Practical implementation methodology using the proposed models has also been discussed along with a numerical example. The results in the numerical example illustrate the control of an epidemic using the optimal policy. Directions for further research and characterization of the optimal policy have also been discussed with the help of the same numerical example. Article Highlights An optimal approach for controlling the spread of an epidemic infection. The approach is able to model the uncertainties involved in the problem. The approach is able to cater for the underlying social network.

Keywords

• Markov decision process
• Epidemics control
• Two-layer networks
• Markov chain approach