A student residence's contact network is modelled as a large Erdos-Renyi graph with…

PHYSICS · Multi-part · Fermi University Physics · Thermal, Statistical & Complex Systems · Complex and collective systems · Complex and collective systems

Many Parts, One Behaviour, Ch Epidemics on networks

Problem

A student residence's contact network is modelled as a large Erdos-Renyi graph with mean degree

c = 6

, so its degree distribution is Poisson with

\langle k^2\rangle = c^2 + c

. A seasonal influenza strain crosses each contact edge with transmissibility

T = 0.3

. ((a)) Find the epidemic threshold

T_{\rm c}

of the network in the locally tree-like approximation. ((b)) Residents are vaccinated at random with a vaccine that fully protects everyone who receives it. Find the smallest coverage that prevents a large outbreak.

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