Mark Newman
- Published in print:
- 2018
- Published Online:
- October 2018
- ISBN:
- 9780198805090
- eISBN:
- 9780191843235
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198805090.003.0015
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics
A discussion of the site percolation process on networks and its application as a model of network resilience. The chapter starts with a description of the percolation process, in which nodes are ...
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A discussion of the site percolation process on networks and its application as a model of network resilience. The chapter starts with a description of the percolation process, in which nodes are randomly removed from a network, and of the percolation phase transition at which a giant percolating cluster forms. The properties of percolation on configuration model networks are studied, including networks with power-law degree distributions, and including both uniform and non-uniform removal of nodes. Computer algorithms for simulating percolation on real-world networks are also discussed, and numerical results are given for several example networks, including the internet and a social network.Less
A discussion of the site percolation process on networks and its application as a model of network resilience. The chapter starts with a description of the percolation process, in which nodes are randomly removed from a network, and of the percolation phase transition at which a giant percolating cluster forms. The properties of percolation on configuration model networks are studied, including networks with power-law degree distributions, and including both uniform and non-uniform removal of nodes. Computer algorithms for simulating percolation on real-world networks are also discussed, and numerical results are given for several example networks, including the internet and a social network.
Mark Newman
- Published in print:
- 2018
- Published Online:
- October 2018
- ISBN:
- 9780198805090
- eISBN:
- 9780191843235
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198805090.003.0016
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics
This chapter discusses the spread of diseases over contact networks between individuals and the methods used to model this process. The chapter begins with an introduction to the classic models of ...
More
This chapter discusses the spread of diseases over contact networks between individuals and the methods used to model this process. The chapter begins with an introduction to the classic models of mathematical epidemiology, including the SI model, the SIR model, and the SIS model. Models for coinfection and competition between diseases are also discussed, as well as “complex contagion” models used to represent the spread of information. The remainder of the chapter deals with the behavior of these models on networks, where the behavior of spreading diseases depends strongly on network structure. It is shown that the SIR model maps to a bond percolation process on networks, allowing us to solve for static properties such as the total number of individuals infected in a disease outbreak. The case of the configuration model is developed in detail and the calculations are extended to competing diseases, coinfection, and complex contagion. Time-dependent behavior of diseases on networks is also studied using various differential equation approximations, including pair approximations and degree-based approximations.Less
This chapter discusses the spread of diseases over contact networks between individuals and the methods used to model this process. The chapter begins with an introduction to the classic models of mathematical epidemiology, including the SI model, the SIR model, and the SIS model. Models for coinfection and competition between diseases are also discussed, as well as “complex contagion” models used to represent the spread of information. The remainder of the chapter deals with the behavior of these models on networks, where the behavior of spreading diseases depends strongly on network structure. It is shown that the SIR model maps to a bond percolation process on networks, allowing us to solve for static properties such as the total number of individuals infected in a disease outbreak. The case of the configuration model is developed in detail and the calculations are extended to competing diseases, coinfection, and complex contagion. Time-dependent behavior of diseases on networks is also studied using various differential equation approximations, including pair approximations and degree-based approximations.
