To mitigate the spread of the COVID-19 coronavirus, some countries have enforced more stringent non-pharmaceutical interventions in contrast to those widely adopted (for e.g. the state of Kuwait). In addition to standard practices such as enforcing curfews, social distancing, and closure of non-essential service industries, other non-conventional policies such as the total confinement of highly populated areas has also been implemented. In this paper, we model the movement of a host population using a mechanistic approach based on random walks, which are either diffusive or super-diffusive. Infections are realised through a contact process, whereby a susceptible host may be infected if in close spatial proximity of the infectious host. Our focus is only on the short-time scale prior to the infectious period, so that no further transmission is assumed. We find that the level of infection depends heavily on the population dynamics, and increases in the case of slow population diffusion, but remains stable for a high or super-diffusive population. Also, we find that the confinement of homogeneous or overcrowded sub-populations has minimal impact in the short term. Finally, we discuss the possible implications of our findings for total confinement in the context of the current situation in Kuwait.