N-strain epidemic model using bond percolation
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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.
Mann , P S , Smith , V A , Mitchell , J B O & Dobson , S A 2022 , ' N-strain epidemic model using bond percolation ' , Physical Review. E, Statistical, nonlinear, and soft matter physics , vol. 106 , no. 1 , 014304 . https://doi.org/10.1103/PhysRevE.106.014304
Physical Review. E, Statistical, nonlinear, and soft matter physics
DescriptionFunding: 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).
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