Mathematical analysis of huanglongbing transmission model in a periodic environment

Huanglongbing infection (HLB) or citrus greening and more rarely yellow shoot disease is a fatal bacterial disease of citrus. Our objective in this study is to propose a mathematical model to predict the outbreak of Huanglongbing (HLB) infection with Logistic growth in psyllid insect vectors to predict the transmission of this disease among citrus. Indeed, we considered the periodic environment to model the seasonality of the spread of the disease. In this regard, an explicit expression of the reproductive number R0 is obtained, which has been used for analyzing the behavior of the model in the cases when R-0 > 1 and R-0 < 1. The mathematical findings are supported using numerical illustrations.