Stochastic Epidemic Models on Complex Network

Abstract

The spread of a virus or the outbreak of an epidemic are natural examples of stochastic processes. Classical mathematical descriptions of such phenomenon include various branching processes such as the SIR (Susceptible-Infected-Recovered) model and the SIS (Susceptible-Infected-Susceptible) model. The basis of this thesis consists of giving a comprehensive overview of the mathematical theory behind these models with an emphasis on the SIR model and its evolution on complex networks. Further, following [1],[2],[3], we consider the evoSIR on three network structures (Erdös Rényi Graph (ER graph), Configuration model network and the preferential attachment model) in which a susceptible after learning the status of his neighbor breaks that connection at rate ρ and rewire to a randomly chosen individual in the population. We show through simulations that, delSIR can reduce the final size of an outbreak of diseases with a higher probability. Finally, we show that the network structure crucially influences the measures to control the outbreak of diseases at the population level.