Threshold behaviour of a stochastic vector plant model for tomato yellow curl leaves disease: a study based on mathematical analysis and simulation

Diseases transmitted by vectors in crops represent a severe risk to the farmer, causing low production and lower quality, which results in a drastic reduction in crop yield. Here we study a stochastic plant-vector-host epidemic model with direct transmission. Perturbing with Brownian motion plant replanting and vector fumigation rates, we formulate an Ito stochastic differential equations that capture the uncertainty of the controls. We derive conditions to assure extinction and persistence of disease using two different stochastic versions of the so-called basic reproductive number. Finally, we verify and illustrate our theory by numerical experiments. Our simulations suggest that uncertainty could drive dramatic stability changes. Because in practice, confirming an infected plant via laboratory tests is not necessarily feasible, replanting and fumigation strategies suffer considerable uncertainty. Here, we quantify and study the impact and consequences of this uncertainty. We conclude that environmental noise promotes dramatic stability changes.