N-strain epidemic model using bond percolation

Peter Stephen Mann; V.A. Smith; John B. O. Mitchell; Simon Andrew Dobson

doi:10.1103/PhysRevE.106.014304

N-strain epidemic model using bond percolation

Peter Stephen Mann^*, V.A. Smith, John B. O. Mitchell, Simon Andrew Dobson

^*Corresponding author for this work

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Abstract

In this paper we examine the structure of random networks that have undergone bond percolation an arbitrary, but finite, number of times. We define two types of sequential branching processes: a competitive branching process - in which each iteration performs bond percolation on the residual graph (RG) resulting from previous generations; and, collaborative branching process - where percolation is performed on the giant connected component (GCC) instead. We investigate the behaviour of these models, including the expected size of the GCC for a given generation, the critical percolation probability and other topological properties of the resulting graph structures using the analytically exact method of generating functions. We explore this model for Erds-Renyi and scale free random graphs. This model can be interpreted as a seasonal
n-strain model of disease spreading.

Original language	English
Article number	014304
Number of pages	20
Journal	Physical Review. E, Statistical, nonlinear, and soft matter physics
Volume	106
Issue number	1
DOIs	https://doi.org/10.1103/PhysRevE.106.014304
Publication status	Published - 20 Jul 2022

Keywords

Complex networks
Epidemic spreading
Percolation
Co-infection

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This output contributes to the following UN Sustainable Development Goals (SDGs)

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10.1103/PhysRevE.106.014304

Mann-2022-N-strain-epidemic-model-PhysRevE.106.014304
Copyright © 2022 American Physical Society. This work has been made available online in accordance with publisher policies or with permission. Permission for further reuse of this content should be sought from the publisher or the rights holder. This is the final published version of the work, which was originally published at https://doi.org/10.1103/PhysRevE.106.014304.
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Science of Sensor System Software: Science of Sensor System Software
Dobson, S. A. (PI)
EPSRC
1/01/16 → 31/12/22
Project: Standard

Cite this

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title = "N-strain epidemic model using bond percolation",

abstract = "In this paper we examine the structure of random networks that have undergone bond percolation an arbitrary, but finite, number of times. We define two types of sequential branching processes: a competitive branching process - in which each iteration performs bond percolation on the residual graph (RG) resulting from previous generations; and, collaborative branching process - where percolation is performed on the giant connected component (GCC) instead. We investigate the behaviour of these models, including the expected size of the GCC for a given generation, the critical percolation probability and other topological properties of the resulting graph structures using the analytically exact method of generating functions. We explore this model for Erds-Renyi and scale free random graphs. This model can be interpreted as a seasonal n-strain model of disease spreading.",

keywords = "Complex networks, Epidemic spreading, Percolation, Co-infection",

author = "Mann, {Peter Stephen} and V.A. Smith and Mitchell, {John B. O.} and Dobson, {Simon Andrew}",

note = "Funding: This work was partially supported by the UK Engineering and Physical Sciences Research Council under grant number EP/N007565/1 (Science of Sensor Systems Software).",

year = "2022",

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T1 - N-strain epidemic model using bond percolation

AU - Mann, Peter Stephen

AU - Smith, V.A.

AU - Mitchell, John B. O.

AU - Dobson, Simon Andrew

N1 - Funding: This work was partially supported by the UK Engineering and Physical Sciences Research Council under grant number EP/N007565/1 (Science of Sensor Systems Software).

PY - 2022/7/20

Y1 - 2022/7/20

N2 - In this paper we examine the structure of random networks that have undergone bond percolation an arbitrary, but finite, number of times. We define two types of sequential branching processes: a competitive branching process - in which each iteration performs bond percolation on the residual graph (RG) resulting from previous generations; and, collaborative branching process - where percolation is performed on the giant connected component (GCC) instead. We investigate the behaviour of these models, including the expected size of the GCC for a given generation, the critical percolation probability and other topological properties of the resulting graph structures using the analytically exact method of generating functions. We explore this model for Erds-Renyi and scale free random graphs. This model can be interpreted as a seasonal n-strain model of disease spreading.

AB - In this paper we examine the structure of random networks that have undergone bond percolation an arbitrary, but finite, number of times. We define two types of sequential branching processes: a competitive branching process - in which each iteration performs bond percolation on the residual graph (RG) resulting from previous generations; and, collaborative branching process - where percolation is performed on the giant connected component (GCC) instead. We investigate the behaviour of these models, including the expected size of the GCC for a given generation, the critical percolation probability and other topological properties of the resulting graph structures using the analytically exact method of generating functions. We explore this model for Erds-Renyi and scale free random graphs. This model can be interpreted as a seasonal n-strain model of disease spreading.

KW - Complex networks

KW - Epidemic spreading

KW - Percolation

KW - Co-infection

U2 - 10.1103/PhysRevE.106.014304

DO - 10.1103/PhysRevE.106.014304

M3 - Article

SN - 1539-3755

VL - 106

JO - Physical Review. E, Statistical, nonlinear, and soft matter physics

JF - Physical Review. E, Statistical, nonlinear, and soft matter physics

IS - 1

M1 - 014304

ER -

N-strain epidemic model using bond percolation

Abstract

Keywords

UN SDGs

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Science of Sensor System Software: Science of Sensor System Software

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