Fractional study of Huanglongbing model with singular and non-singular kernel. (English) Zbl 1485.92142
Summary: The disease of citrus is Huanglongbing (HLB), a Chinese name meaning yellow shoot disease and in English-speaking countries referred as a citrus greening threatening the citrus industries worldwide. Citrus greening associated with ‘Candidatus Liberibacter asiaticus’ (CLas), is the most devastating disease spread through the infected citrus trees and the major insect vector, the infected citrus psyllid (Diaphorina citri). A fractional-order compartmental model in Caputo and Atangana-Baleanu sense is consider to study the dynamical aspects of HLB among citrus trees and Asian citrus psyllid (ACP). We computed a basic reproduction number and present a detailed theoretical analysis including solution positivity and the stability of disease-free equilibrium of the Caputo fractional model. Numerical simulations are conducted for both Caputo and Atangana-Baleanu operators. The numerical results of Caputo model suggest that the infection and removal rate impacts impressively on the severity of the HLB. Moreover, for different values of the fractional derivative suggest the infection minimization and possibly the control for the disease. While simulating the model using both the operators, the results captured are are better and may be useful in further research of the proposed model. We conclude that, the Atangana-Baleanu operator is more effective and prominent biologically as compared to the Caputo derivative for the proposed problem.
MSC:
| 92D30 | Epidemiology |
| 92C80 | Plant biology |
| 34A08 | Fractional ordinary differential equations |
| 34D35 | Stability of manifolds of solutions to ordinary differential equations |
Keywords:
greening citrus; stage-structured model; liberibacter; Asian citrus psyllid; Caputo fractional derivative; Atangana-Baleanu fractional derivative; simulationSoftware:
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