Aims. Meteoroid trails ejected during past perihelion passages of the Mars-orbit-intersecting comet 79P/du Toit-Hartley have the potential of generating meteor outbursts in the Martian atmosphere. Depending on timing and intensity, the effects of these outbursts may be detectable by instrumentation operating in the vicinity of Mars. We aim to generate predictions for meteor activity in the martian atmosphere related to that comet; to search for evidence, in planetary mission data, that such activity took place; and to make predictions for potentially detectable future activity. Methods. We have modelled the stream by integrating numerically the states of particle ensembles, each ensemble representing a trail of meteoroids ejected from the comet during 39 perihelion passages from 1803, and propagated them forward in time, concentrating on those particles that physically approach Mars in the recent past and near future. Results. We find several instances where meteor outbursts of low to moderate intensity may have taken place at Mars since 1997. A search through Mars Global Surveyor (MGS) radio science data during two periods in 2003 and 2005 when data coverage was available showed that a plasma layer did indeed form in the martian ionosphere for a period of a few hours in April 2003 as a direct consequence of the predicted outburst. The apparent failure to identify such an event in 2005 could be due to those meteoroids ablating lower in the atmosphere or that the cometary dust follows a different particle size distribution than what was assumed. Our study highlights the need for further theoretical modelling of the response of the martian ionosphere to a time-variable meteoroid flux, observations of the comet itself and, most importantly, regular monitoring of the martian ionosphere during future outbursts predicted by our model.