Numerous factors influence the likelihood of contact between susceptible and infectious people, including participation in different social activities, cultural barriers such as membership of particular ethnic groups with associated customs, or separation due to geographic distance. These factors guarantee that contact among individuals within a population is distinctly nonrandom. Results from several theoretical studies show that nonrandom mixing among subgroups has many consequences for the outcome of epidemic spread, including affecting the time at which a disease is introduced into different subgroups and the speed of propagation and severity of an epidemic.
Most recent models for the spread of infectious diseases in human populations incorporate nonrandom patterns of mixing across subgroups and include a parameter for contact between groups that depends on the subgroups from which the susceptible and infective individuals derive. This parameter represents only the end result of the mixing process, leaving implicit the mechanism by which contact occurs. Here we describe a model that explicitly incorporates the mechanism for contact among individuals from different subgroups. Contact between individuals occurs as a result of the mobility of participants across either geographic or social space. Because it is simpler to visualize, we limit our discussion here to geographic mobility. Models for behavioral mobility are straightforward adaptations of this process (e.g. Sattenspiel and Castillo-Chavez 1990, Jacquez et al 1989).
Consider a population that is distributed among n regions. Individuals from region i leave the region at a rate σi per unit time. These visitors are then distributed among the n – 1 destinations with probabilities vij to each destination j.