# Mixing and Infection in a Two-Group SIS Model

Mixing and Infection in a Two-Group SIS Model

Consider a population composed of two groups of equal size (designated 1 and 2), in which individuals can be either "infected" or "susceptible." In each time period, each individual has a probability of interacting with another individual. With probability , this interaction is with an individual of the other group. Susceptible individuals become infected only if they interact with an infected individual, and in that case they do so with probability , where denotes the individual's group. Infected individuals become susceptible with probability .

p

m

υ

i

i=1,2

δ

i

This Demonstration shows the proportion of infected individuals in each group (and in the total population ) at the nearly globally asymptotically stable state of the mean dynamics, as a function of the level of mixing between the two groups (i.e. the percentage of interactions that occur between individuals of different groups). The two relevant parameters are the effective infection rates of each group: .

ρ

i

ρ

pop

λ=pυ/δ

i

i

i