  Various theoretical models have been proposed to understand the basic nature
of epidemics. Recent studies focus on the effects of mobility to epidemic
process. However, uncorrelated random walk is typically assumed as the type of
movement. In our daily life, the movement of people sometimes tends to be
limited to a certain direction, which can be described by biased random walk.
Here, we developed an agent-based model of susceptible-infected-recovered (SIR)
epidemic process in a 2D continuous space where agents tend to move in a
certain direction in addition to random movement. Moreover, we mainly focus on
the effect of the reduced mobility of infected agents. Our model assumes that,
when people are infected, their movement activity is greatly reduced because
they are physically weakened by the disease. By conducting extensive
simulations, we found that when the movement of infected people is limited, the
final epidemic size becomes small. However, that crucially depended on the
movement type of agents. Furthermore, the reduced mobility of infected agents
lengthened the duration of the epidemic because the infection progressed
slowly.
