To send content items to your account,
please confirm that you agree to abide by our usage policies.
If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account.
Find out more about sending content to .
To send content items to your Kindle, first ensure email@example.com
is added to your Approved Personal Document E-mail List under your Personal Document Settings
on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part
of your Kindle email address below.
Find out more about sending to your Kindle.
Note you can select to send to either the @free.kindle.com or @kindle.com variations.
‘@free.kindle.com’ emails are free but can only be sent to your device when it is connected to wi-fi.
‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.
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.