To analyze the parameter dependence of the model, we consider four "disease transmission regimes", where both recovery and social transmission rate take on high or low values. A high recovery rate means that typical recovery times are similar to to the time needed to move between areas, so that recovery is likely to occur during migration. A high infection rate means that an epidemic can spread through the population before individuals are able to move away from the group or to the recovery area. A low recovery rate means that recovery is unlikely to occur during migration, and that an individual must spend a significant amount of time in the recovery area in order to become healthy once again. A low infection rate means that if individuals change their motion after infection, it is possible to move away from other groupmates before infecting them. Using these definitions, we can define four different disease transfer regimes for each model:
- High rates: High infection rate / High recovery rate
- High recovery: Low infection rate / High recovery rate
- High infection: High infection rate / Low recovery rate
- Low rates: Low infection rate / Low recovery rate
Social influence to motion has a different effect on the fraction infected in each of these cases. With high rates, there are transient epidemics that die quickly, because the infected recover quickly (Fig 2a). Because infection and recovery happen quickly, the group most often stays together as a whole, which often consists of both healthy and infected individuals, and (migratory recovery)
([JD: remember that you wrote summary on page of notebook with blue sticky note]])
In regime 2, low overall infection prevalence
in regime 3, oscillatory infections. There is an epidemic, then the group moves 'together' to the recovery area. Then, move back as recover. At high social though, the group can never split apart, and as a result, recovered individuals don't leave infected individuals while in the recovery area, and then become re-infected. This causes the whole group to essentially stay infected
in regime 4, also oscillatory (?)
The 1D model can capture the mechanisms of what is seen in regimes (3 - only 3??), but not others. This is because the model does not allow realistic group fission. Without noise, there is a fixed threshold at which an individual can break off from the group. In contrast, in the more realistic 2D model, there is randomness to individual motion, and so there is always a small probability that an individual will break off from the group.
[[or, to address this, should I add noise to the 1D model? An easy way would be to add the noise, but still enforce the positional limits of -1 and 1. Then wouldn't have to deal with drift]]
The 1D model shows that when social weight increases, there can be "transient epidemics" due to social influence to motion. For example, a newly infected individual has a conflicting preference of whether to move to the recovery area or to remain near groupmates, and this causes it to remain by others until enough have become infected that a sub-group reaches consensus to move together to the recovery area. ....Other explanation of 1D model results.... (Figure \ref{302067}).
Additionally we consider effect of a "reaction time offset", between when an individual becomes infected, and when their personal location preference changes. (Figure \ref{302067}C).