Mathematical model of coffee tree's rust control using snails as biological agents

Abstract

Coffee rust is one of the main diseases that affect coffee plantations worldwide, causing large-scale ecological and economic damage. While multiple methods have been proposed to tackle this challenge, using snails as biological agents have shown to be the most consistent and promising approach. However, snails are an invasive species, and overusing them can cause devastating outcomes. In this paper, we develop and explore an ecological-epidemiological mathematical model for the coffee tree rust pandemic control using snails as biological agents. We analyze the equilibria of the proposed system with their stability properties. In addition, we perform numerical analysis to obtain the sensitivity of the system to different changes and manipulation of the snails pandemic control, under specific conditions. Finally, we propose an in silico mechanism to obtain an analytical connection between the system's initial condition and the number of snails needed to optimally control the rust pandemic spread while preventing the snail population to grow unmanageably. Our model can be used to optimize the usage of snails as biological agents to control the rust pandemic in spatially-small areas, by predicting the number of snails one needs to introduce to the ecosystem in order to obtain a desired outcome.

Keywords: Biological agent control; Coffee rust pandemic; Optimal pandemic control policy; SIS-LV model.