Modelling the spread of infections when the contact rate among individuals is short ranged: Propagation of epidemic waves

Integral equations for the force of infection were derived taking into account spatial variables. Those equations were studied both numerically and with functional analysis techniques. Threshold conditions for the establishment of the infection were also derived. The existence of travelling waves of the infection was investigated. An integral equation for the shape of the wave front was deduced. Conditions for the existence of those waves were derived independently of the velocity of propagation. The model differs from previous studies in that we allow recovery from the infectious status and/or demographic structure in the host population, that is, deaths and births of individuals.