Epidemic R0 from Graph Degree

Problem

Estimate the basic reproduction number of an SIR process from the mean degree: R0 = beta * mean_degree / gamma.

beta is the transmission rate per edge, gamma the recovery rate, and edges the contact list of an undirected graph with n nodes. Return the float value, or 0.0 when n is 0 or gamma is 0.

Hint

A denser contact network raises R0 and makes outbreaks harder to contain.

Test cases

case 1

in: [3,[[0,1],[1,2]],0.5,0.25]

expected: 2.6666666666666665

case 2

in: [4,[[0,1],[0,2],[0,3]],0.2,0.5]

expected: 0.6000000000000001

case 3

in: [1,[],0.5,0.25]

expected: 0

case 4

in: [4,[[0,1],[0,2],[0,3],[1,2],[1,3],[2,3]],0.3,0.2]

expected: 4.5

Starter codePython

def epidemic_r0(n, edges, beta, gamma):
    # Your code here
    pass

4 test cases · run your code against them in the editor