## How are epidemic models simulated in case of mobility?

I am not a mathematician but out of curiosity I am trying to implement the SIS epidemic model when the nodes have mobility to understand how it will change the results. I understand how to perform this simulation in an analytical fashion. However, things get rather confusing when nodes are mobile. To give a background, all models that I have come across do not consider that nodes are mobile.

The model assumes that each node can infect any node and hence the equations (differential or difference) are valid. But when nodes are mobile, each node is not able to infect every other node (the other node might not be within the range) and has to explicity send a message to a node that is susceptible in order to infect it. In that case, give an infection rate B, how do I simulate this when the nodes are mobile?

Currently, the way I am doing this is in the following way:

def Controller():
for i in range(1,100):
randNum = getRand()
if (randNum <= InfectionRate):
neighbors = getNeighbors(i)
ScheduleTransmission(getCurrentTime(), i, neighbors)
Schedule(getCurrentTime() + 1, Controller)


My problem is that I am not understanding if the infection rate can now be captured through a single value (which was previously B). If not, how does one analyze this scenario? Do I set the InfectionRate as B/numNodes so that the overall probability will be B? Any suggestions?

UPDATE: Making it more realistic

def Controller():
for i in range(1,100):
neighbors = getNeighbors(i)
for j in neighbors:
randNum = getRand()
if (randNum <= InfectionRate):
ScheduleTransmission(getCurrentTime(), i, j)
Schedule(getCurrentTime() + 1, Controller)

-

You are free to define the parameters as you wish, as long as you document it. But in the standard (non-spatial) SIS model the rate at which new infections occur is $\beta I S$, i.e. each infective individual infects each susceptible individual at a rate $\beta$. This would correspond in your model to a situation where all individuals are neighbours and at each time step an infective node sends a message to each neighbour with probability $\beta \Delta t$, where $\Delta t$ represents the duration of one time step.