Plant qualitative resistances to viruses are natural exhaustible resources that can be impaired by the emergence of resistance-breaking (RB) virus variants. Mathematical modelling can help determine optimal strategies for resistance durability by a rational deployment of resistance in agroecosystems. Here, we propose an innovative approach, built up from our previous empirical studies, based on plant cultivars combining qualitative resistance with quantitative resistance narrowing population bottlenecks exerted on viruses during host-to-host transmission and/or within-host infection. Narrow bottlenecks are expected to slow down virus adaptation to plant qualitative resistance. To study the effect of bottleneck size on yield, we developed a stochastic epidemic model with mixtures of susceptible and resistant plants, relying on continuous-time Markov chain processes. Overall, narrow bottlenecks are beneficial when the fitness cost of RB virus variants in susceptible plants is intermediate. In such cases, they could provide up to 95 additional percentage points of yield compared with deploying a qualitative resistance alone. As we have shown in previous works that virus population bottlenecks are at least partly heritable plant traits, our results suggest that breeding and deploying plant varieties exposing virus populations to narrowed bottlenecks will increase yield and delay the emergence of RB variants. This article is part of the theme issue ‘Modelling infectious disease outbreaks in humans, animals and plants: approaches and important themes’. This issue is linked with the subsequent theme issue ‘Modelling infectious disease outbreaks in humans, animals and plants: epidemic forecasting and control’.