Seeding the network with specific points of infection

Problem: You want to control where the infection initially starts, for example to put the infected nodes in an “unusual” place to study how that affects the epidemic.

Solution: Let’s assume we’re running an SIR model. By default the CompartmentedModel infects a random fraction of nodes according to the value of the SIR.P_INFECTED parameter. If you want to take control then two things need to happen:

1. Inhibit random infections

2. Decide on and infect the specific nodes of interest

A common sub-case of this approach is to infect exactly one node at random. One could do this by setting SIR.P_INFECTED to \(\frac{1}{N}\), but that runs the risk of infecting not exactly one node – and if you happen to infect no nodes, everything will break.

There are several ways to implement this depending on exactly what you want to accomplish, the easiest of which is to directly code the required behaviour in a sub-class of the model you want to seed. (We’ll assume an SIR model: change parameter names accordingly for other models.)

Changing the initial seeding procedure

To take control of the seeding procedure we have to account for the compartments of all the nodes – not just the infected ones. We can do this by overriding CompartmentedModel.initialCompartments(). If, for example, we wanted exactly one seed node, chosen at random, then we could do the following:

from epydemic import rng       # the random number generator

def build(self, params):
    '''Build the network without any initial random infection.

    :param params: the experimental parameters'''
    params[self.P_INFECTED] = 0.0
    super().build(params)

def initialCompartments(self):
    '''Infect exactly one node, chosen at random.'''
    g = self.network()
    ns = set(g.nodes())
    N = len(ns)

    # choose one node and infect it
    n = rng.integers(N)
    self.changeInitialCompartment(n, self.INFECTED)

    # mark all other nodes as susceptible
    ns.remove(n)
    for n in ns:
        self.changeInitialCompartment(n, self.SUSCEPTIBLE)

(We’ve imported epydemic’s global random number generator from which we draw the numbers we need.) Overriding CompartmentedModel.build() inhibits random seeding by setting the probability to zero. (We have to do this as the SIR.build() method sets the initial distribution and so accesses the SIR.P_INFECTED parameter – and fails if it isn’t set. Other compartmented models do the same.)

The overridden CompartmentedModel.initialCompartments() first chooses a node, marks it as infected, and then marks all other nodes as susceptible. You would of course need to change this if there was some other compartment that might be set from the initial compartment distribution.