Aviation emissions of aerosol particles and aerosol precursor gases alter the Earth's radiation budget via both direct and indirect aerosol effects, resulting in a significant climate effect. Current estimates of aviation-induced climate effects are based on coarse-resolution global aerosol-climate models, which are not able to resolve the microphysical processes at the aircraft plume scale. This results in large uncertainties in the aviation-induced impact on aerosol number and size, which are key quantities for estimating the aerosol indirect effect, especially for low-level liquid-phase clouds. In this work, a double-box aircraft exhaust plume model is developed to explicitly simulate the aerosol microphysics inside a dispersing aircraft exhaust plume, together with a simplified representation of the vortex regime (which begins ĝ1/4 10 s after the aircraft emissions and captures the dynamics of aerosol particle interactions with contrail ice particles). The aircraft exhaust plume model is used to quantify the aviation-induced aerosol number concentration at the end of the dispersion regime (ĝ1/446 h) and the results are compared with the result obtained by the instantaneous dispersion approach commonly applied by the global models. The difference between the plume approach (simulated using two boxes) and the instantaneous dispersion approach (simulated by a single box) is defined as the plume correction: for typical cruise conditions over the North Atlantic and typical aviation emission parameters, the plume correction for aviation-induced particle number concentration ranges between -15 % and -4.2 %, depending on the presence or absence of the contrail ice in the vortex regime, respectively. A tendency-based process analysis shows that the negative value of the plume correction is due to the higher efficiency of coagulation and nucleation processes in the plume approach, leading to lower total particle number concentrations compared to the instantaneous dispersion approach. Sensitivity studies over different regions highlight the role of background conditions for the plume microphysics, with the plume correction varying between -12 % for Europe and -42 % for China in a scenario with contrail ice in the vortex regime. Parametric studies performed on various aviation emission parameters used to initialise the plume model demonstrate the high relevance of contrail ice in the vortex regime to considerably reduce the aviation-induced aerosol number concentration in the plume approach. Moreover, the parametric studies show a large sensitivity towards aviation fuel sulfur content, driving sulfur dioxide (SO2) emissions and the sulfuric acid (H2SO4) formation, which in turn is a primary driver for the nucleation process. Thanks to its flexible configuration and minor additional computational costs, the plume model presented here can readily be applied in coarse-resolution global aerosol-climate models or used as offline parametrisation to quantify the climate effects of aviation-induced aerosol particles.