A Model of the Epidemiology of Greening in Florida Citrus Groves and Its Economic Implications

Transcription

1 A of the Epidemiology of Greening in Florida Citrus Groves and Its Economic Implications Charles B. Moss 1 and Andrew Schmitz 1 1 University of Florida March 26, 2014

2 1 Citrus Maladies Citrus Greening - The Disease Canker - The Other Citrus Disease Response - Management Alternatives 2 Alternative s Greening and Latency Spatial Economic 3 Tree Infections 4

3 Citrus Maladies Citrus Maladies Citrus Greening - The Disease Canker - The Other Citrus Disease Response - Management Alternatives Agronomic/Weather Freezes January 1981, December 1983, January 1985, December 1989 Citrus Canker Most recently beginning in 2000 (declared uncontrollable in 2006) Huanglongbing or citrus greening Economics Increased trade Diet fads Decreased housing prices in Florida

4 Citrus Greening - The Disease Citrus Maladies Citrus Greening - The Disease Canker - The Other Citrus Disease Response - Management Alternatives Bacterium Candidatus Liberibacter asiaticus Asiatic citrus psyllid (Diaphorina citri Kywayama) This insect was first found in Florida in 1998, and at that time was considered to be a pest of minor importance since the HLB pathogen was not known to be present. The 2005 discovery of HLB in Florida changed the status of this insect to a pest of great importance (Spann et al. 2014, p. 1). Effect of disease Phloem blockage typically leading to loss of root structure Misshapen and bitter fruit Tree decline and death

5 Canker - The Other Citrus Disease Citrus Maladies Citrus Greening - The Disease Canker - The Other Citrus Disease Response - Management Alternatives Causes problems with the marketability of fresh fruit Florida experienced periodic bouts Citrus Health Response Program (CHRP) Handling recommendations 1900 foot kill zones Difficulties Florida hurricanes (2004 Charley, Frances, Ivan and Jeanne) Emergence of backyard citrus CHRP abandoned in 2006.

6 Response - Management Alternatives Citrus Maladies Citrus Greening - The Disease Canker - The Other Citrus Disease Response - Management Alternatives Remove infected tree Remove infected tree and neighbors (similar to canker program) Foliar feed and increased spraying

7 ing the Disease Alternative s Greening and Latency Spatial Economic Reed-Frost model A chain binomial model, sort of a Markov Process x 1t x 2t x 3t x 4t = 1 α 1 α α 2 α α 3 α 3 x 1,t 1 x 2,t 1 x 3,t 1 x 4,t 1 Celluar Automata Basically complicate the Reed- Frost model with transmission to adjacent cells Spatial Autocorrelation Anselin (1)

8 Greening and Latency Alternative s Greening and Latency Spatial Economic Infected trees do not appear infected for some time Logit discovery function zt denotes actually infected, z t is appears infected P z (t, t 0 ) = exp (α 0 + α 1 (t t 0 )) 1 + exp (α 0 + α 1 (t t 0 )). (2) Draw u 1,t U [0, 1] if u 1,t P z (t, t 0 ) the tree exhibits infected. No false positives

9 Spatial Alternative s Greening and Latency Spatial Economic Following Anselin z t = (I ρw ) 1 ( ) ξ t z t 1 If zt 1 = 1 (the tree is infected) ξ ( ) t z t 1 N (0, 1), else ξ t = 0. The spatial matrix W is based on distance W ij (d, δ) = exp (δd ij ). (3)

10 Econonomic Alternative s Greening and Latency Spatial Economic Yield function based on tree age y (a it ) = β 0 2 [1 + tanh (β 1 + β 2 a it )] (4) Disease loss function L (t, t 0, γ) = exp ( γ (t t 0 )) (5) Present value of management scenario ] PV (m) = (1 + R) [p t y it (a it, zt, t 0, m) r t (m) FC t=1 i=1 (6)

11 5 Year Spread Tree Infections Actual Observed

12 10 Year Spread Tree Infections Actual Observed

13 Tree Infections Table 1. Annualized Present Value of Management Strategy Damage Rate Expected Variance Expected Variance No Action , , , , Remove Infected Tree , , , , Remove Neighbor , , , , ,

14 While we have not modeled the foliar feed and spray scenario (yet) the results strongly support this management strategy. The issue is truly private versus social cost. The returns to eradicating greening are large (the annaulized net present value of the grove is $ 3, per acre implying a gain of $ 1, per acre to eradicating the disease at 5 percent loss). However, the private cost to removing a producing tree is high.