Stochastic Epidemic Models on Complex Network
MetadataShow full item record
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 ,,, 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.
Master's thesis in Mathematics and Physics