  Disease outbreaks, such as those of Severe Acute Respiratory Syndrome in 2003
and the 2009 pandemic A(H1N1) influenza, have highlighted the potential for
airborne transmission in indoor environments. Respirable pathogen-carrying
droplets provide a vector for the spatial spread of infection with droplet
transport determined by diffusive and convective processes. An epidemiological
model describing the spatial dynamics of disease transmission is presented. The
effects of an ambient airflow, as an infection control, are incorporated
leading to a delay equation, with droplet density dependent on the infectious
density at a previous time. It is found that small droplets ($\sim 0.4\ \mu$m)
generate a negligible infectious force due to the small viral load and the
associated duration they require to transmit infection. In contrast, larger
droplets ($\sim 4\ \mu$m) can lead to an infectious wave propagating through a
fully susceptible population or a secondary infection outbreak for a localised
susceptible population. Droplet diffusion is found to be an inefficient mode of
droplet transport leading to minimal spatial spread of infection. A threshold
air velocity is derived, above which disease transmission is impaired even when
the basic reproduction number $R_{0}$ exceeds unity.
