Reduced mobility of infected agents suppresses but lengthens disease in biased random walk

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.