Abstract
An epidemic model which describes Huanglongbing transmission is proposed with the goal of investigating the effect of quarantine measures on the spread of diseases. First of all, the analytical formula for the basic reproduction number R0 is obtained by the means of next generation matrix, and the existence of disease-free equilibrium and endemic equilibrium is discussed. Then, the local stability and the global stability of equilibria are investigated by using Routh-Hurwitz criterion and Lyapunov function, respectively. Numerical simulations indicate that comprehensive quarantine measures can effectively control the spread of Huanglongbing. It provides a reliable tactic basis for preventing the epidemic outbreak.
Highlights
The citrus Huanglongbing (HLB), allied with the bacterium Candidatus Liberibacter asiaticus (CLas), poses a great threat to the industry of citrus worldwide [1] [2]
An epidemic model which describes Huanglongbing transmission is proposed with the goal of investigating the effect of quarantine measures on the spread of diseases
Numerical simulations indicate that comprehensive quarantine measures can effectively control the spread of Huanglongbing
Summary
The citrus Huanglongbing (HLB), allied with the bacterium Candidatus Liberibacter asiaticus (CLas), poses a great threat to the industry of citrus worldwide [1] [2]. Jacobsen et al established a 6-dimensional dynamic model within a citrus orchard and analyzed how the number of each class changes over time due to bacterial transmission between citrus trees and psyllids [7]. The quarantine measures, which began on June 17, 2010, were designed to prevent the transportation of citrus in Florida [7]. Motivated by these researches, we propose a dynamic model of HLB with quarantine measures for exposed and infected citrus trees, and perform some theoretical analysis of its properties.
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