Bananas and plantains are a staple food crop in many countries in the tropics. Burrowing nematodes feed on banana roots, among other plants, and create major damages. As they spend most of their life cycle in the roots, their control is particularly challenging. To tackle this issue, we developed a model describing the interactions between roots and nematode during a cropping season. This model considers a variable infestation density, a fairly original modelling feature in plant epidemiology. We analysed this model and studied its asymptotic properties. We showed that the model can exhibit a backward bifurcation, making it difficult to control the pest. We then introduced a control variable, which reduces nematode infestation. This type of control can be achieved by biostimulants, which activate plant defence mechanisms and hence have a nematode suppressive effect. We used optimal control theory to determine how best to apply this control. Using a crop yield proxy, our aim was to maximise the profit while minimising the final nematode population, to ensure minimal infestation and reasonable yield for the next cropping season.