Controlling infectious disease outbreak in a community using a new technique

Abstract

The problem of removing or blocking the minimum number of individuals to control the infectious spread in the network is an NP-hard problem. In this paper a heuristic algorithm, named, BDEC, based on the Principal Component Analysis (PCA) is introduced to deal with this problem. A mathematical model with a PCA approach is formulated, the dynamical behaviour of the model is studied, and also the basic reproductive number R₀ is determined. It is proved that the disease-free equilibrium is stable if R₀ < 1, and it is unstable if R₀ > 1. Then, we introduce a function to discuss the rate of epidemic spread in the social networks by simulation the epidemic spread based on the birth and death process.

Subject Classification:

• 60J20
• 05C82
• 92D30

Keywords:

• Network theory
• Epidemiology
• Basic reproductive number
• Birth and death process