Assessing black rust spreading in wheat production using mathematical model

Abstract

This paper presents and examines a model for a black rust (Puccinia graminis) epidemic in wheat. The spread of black rust can lead to significant yield losses, adversely affecting food security and agricultural economies. Furthermore, controlling the epidemic requires substantial resources, posing challenges for sustainable agricultural practices. The model used in this research comprises three compartments representing susceptible, infected, and recovered wheat. Initially, we will address the well-posedness of the proposed model, focusing on classical results related to existence, positivity, and boundedness. For the analysis of local stability, we identify two equilibria: the disease-free equilibrium and the endemic equilibrium. The local stability of each equilibrium is shown to depend on the basic reproduction number. Numerical simulations are conducted, demonstrating that the numerical results align well with the theoretical findings.