Diffusion Model for Describing the Regional Spread of Huanglongbing from First-Reported Outbreaks and Basing an Area Wide Disease Management Strategy.

Huanglongbing (HLB), a recent worldwide spreading disease on citrus, was detected in July 2009 in Yucatan State of Mexico. The objective of this study was to evaluate the fit of diffusion and classic disease gradient models to large-scale HLB spatial data originated from initial foci to improve sampling, monitoring, and control strategies for Diaphorina citri, vector of Candidatus Liberibacter asiaticus (CLas), putative agent of HLB. Four transect routes were selected: Yuc-1, Yuc-2, QRoo-1, and QRoo-2, based on the directionality of the prevailing winds and foci location of HLB infected plants. In these routes, 35 sites, 5 to 20 km apart, were selected for monthly evaluation during a 12-month period. A 10-insect sample and disease incidence and severity of HLB, further confirmed by PCR, were assessed per site. Mexican lime was more vulnerable (67.5%) than sweet orange (14%). Also, leaf symptoms were mostly found with homogeneous distribution but rarely reaching 100% of the tree canopy during the 12-month period. The diffusion model provided the best fit among the family of time-gradient curves (r2 = 0.90 to 0.99) due to the flexibility of a three-parameter model. The gradients were well conformed to the model in a 25 to 82.6 km range, having the east-west direction the longest effect. Yuc-2 and QRoo-2 transects showed 82.6 and 43.9 km gradients with a diffusion coefficient (Do) of 0.15 and 0.09, respectively. This study constitutes the first quantitative evidence of the regional spread of CLas from a single focus and the application of a flexible model that improved the fit and allowed to better compare different gradients. These results are useful to determine the size of Regional Areas of Diaphorina citri Control (ARCO), a management program currently implemented in Mexico to combat HLB.

A phytoplasma closely related to the pigeon pea witches'-broom phytoplasma (16Sr IX) is associated with citrus huanglongbing symptoms in the state of São Paulo, Brazil.

In February 2007, sweet orange trees with characteristic symptoms of huanglongbing (HLB) were encountered in a region of São Paulo state (SPs) hitherto free of HLB. These trees tested negative for the three liberibacter species associated with HLB. A polymerase chain reaction (PCR) product from symptomatic fruit columella DNA amplifications with universal primers fD1/rP1 was cloned and sequenced. The corresponding agent was found to have highest 16S rDNA sequence identity (99%) with the pigeon pea witches'-broom phytoplasma of group 16Sr IX. Sequences of PCR products obtained with phytoplasma 16S rDNA primer pairs fU5/rU3, fU5/P7 confirm these results. With two primers D7f2/D7r2 designed based on the 16S rDNA sequence of the cloned DNA fragment, positive amplifications were obtained from more than one hundred samples including symptomatic fruits and blotchy mottle leaves. Samples positive for phytoplasmas were negative for liberibacters, except for four samples, which were positive for both the phytoplasma and 'Candidatus Liberibacter asiaticus'. The phytoplasma was detected by electron microscopy in the sieve tubes of midribs from symptomatic leaves. These results show that a phytoplasma of group IX is associated with citrus HLB symptoms in northern, central, and southern SPs. This phytoplasma has very probably been transmitted to citrus from an external source of inoculum, but the putative insect vector is not yet known.

Spatial pattern analysis of citrus canker-infected plantings in são paulo, Brazil, and augmentation of infection elicited by the asian leafminer.

ABSTRACT Eradication of Asiatic citrus canker (ACC) has become increasingly difficult over the last decade, following the introduction of the Asian leafminer into Brazil and Florida, which has led to changes in the eradication protocols. The present study, undertaken in Brazil, was aimed at characterizing the spatial patterns of ACC in commercial citrus plantings to gain better understanding of the dynamics of the disease subsequent to introduction of the leafminer. The spatial patterns of ACC were mapped in 326 commercial citrus plantings and statistically assessed at various spatial dimensions. The presence of "within-group" aggregation in each plot was examined via beta-binomial analysis for groups of trees parsed into three-by-three-tree quadrats. The relative intensity of aggregation was expressed as a binomial index of dispersion (D) and heterogeneity among plots expressed as the intracluster correlation coefficient, rho. The population of data sets was found to fall into three D categories, D < 1.3, 1.3 3.5. These categories then were related to other spatial characteristics. The binary form of Taylor's power law was used to assess the overdispersion of disease across plots and was highly significant. When the overall population of plots was parsed into D categories, the Taylor's R (2) improved in all cases. Although these methods assessed aggregation well, they do not give information on the number of foci or aggregations within each plot. Therefore, the number of foci per 1,000 trees was quantified and found to relate directly to the D categories. The lowest D category could be explained by a linear relationship of number of foci versus disease incidence, whereas the higher two categories were most easily explained by a generalized beta function for the same relationship. Spatial autocorrelation then was used to examine the spatial relationships "among groups" composed of three-by-three-tree quadrats and determine common distances between these groups of ACC-infected trees. Aggregation was found in >84% of cases at this spatial level and there was a direct relationship between increasing D category and increasing core cluster size, and aggregation at the among-group spatial hierarchy was generally stronger for the within-row than for the across-row orientation. Clusters of disease were estimated to average between 18 and 33 tree spaces apart, and the presence of multiple foci of infection was commonplace. The effectiveness of the eradication protocol of removing all "exposed" trees within 30 m surrounding each "ACC-infected tree" was examined, and the distance of subsequent infected trees beyond this 30-m zone from the original focal infected tree was measured for each plot. A frequency distribution was compiled over all plots to describe the distance that would have been needed to circumscribe all of these outliers as a theoretical alternative protocol to the 30-m eradication protocol. The frequency distribution was well described by a monomolecular model (R(2) = 0.98) and used to determine that 90, 95, and 99% of all newly infected trees occurred within 296, 396, and 623 m of prior-infected trees in commercial citrus plantings, respectively. These distances are very similar to previously reported distances determined for ACC in residential settings in Florida.

Effect of Citrus Sudden Death on Yield and Quality of Sweet Orange Cultivars in Brazil.

Citrus sudden death (CSD) has greatly affected sweet orange cultivars grafted on Rangpur lime in São Paulo and Minas Gerais States, Brazil. To characterize and quantify CSD damage, fruit yield and quality were assessed in each combination of sweet orange cultivar (Hamlin, Pera, Natal, and Valencia), age class (3 to 5, 6 to 10, and 11 to 15 years old), and CSD severity class (0 = no symptom, 1 = initial symptoms, and 2 = severe symptoms). For each combination, 10 trees were harvested and 20 fruit were taken for quality analysis. Damage was characterized by reduction of: (i) total weight of fruit/tree (36 and 67% for severity class 1 and 2, respectively), (ii) number of fruit/tree (27 and 55%), (iii) fruit size (13 and 25% in diameter and height [stem to styler distance]), (iv) fruit weight (32 and 56%), (v) total soluble solids (TSS)/fruit (18 and 42%), and increase of (vi) Brix (14 and 34%), (vii) acidity (16 and 41%), and (viii) TSS/90-lb. box (21 and 33%). There was no alteration on Brix/acidity ratio and percentage of juice on fruit of affected trees. Sweet orange cultivars did not differ in percentage of reduction or increase of all yield and quality variables, with the exception of Pera, which expressed increases of Brix and acidity. For more severe affected trees, the youngest plants showed a higher reduction in fruit number/tree, whereas plants 6 to 10 years old showed a higher increase in fruit acidity and TSS/box. However, no differences in percentage of reduction or increase for other variables were observed among different age classes. The damage to the above probably was associated with reduced water absorption capacity of CSD-affected trees.

Spatial Pattern of Trees Affected by Black Spot in Citrus Groves in Brazil.

Citrus black spot (CBS), caused by Guignardia citricarpa, is the most important fungal disease of orange trees in Brazil. The spatial pattern of CBS-symptomatic trees was evaluated using the binomial dispersion index (D), Ripley's K function (K), and a Monte Carlo test for minimum mean distance (d) to understand the distribution of the pathogen. Disease was monitored in 7,790 citrus trees from four commercial groves. In one grove, disease incidence was assessed from 1999 to 2001 and, in the others, disease assessments were conducted only in 2002. Infected trees were aggregated based on the three statistical analyses used (D, K, and d) regardless of the CBS incidence. The binomial index of dispersion (D) indicated aggregation of CBS-affected trees for all groves and for various quadrat sizes (2 by 2, 3 by 3, 4 by 4… up to 10 by 10). According to Ripley's K function, the dependence among symptomatic trees comprised two to three neighboring trees. Disease dispersion occurred at distances below 24.7 m according to the test for d. This suggests that the dispersion of inoculum is highly important over short distances. As a consequence, the required sample size to achieve a level of accuracy of C = 20% increases exponentially with the decrease in incidence of CBS below 15% infected plants.

Sudden Death of Citrus in Brazil: A Graft-Transmissible Bud Union Disease.

Citrus Sudden Death (CSD), a new, graft-transmissible disease of sweet orange and mandarin trees grafted on Rangpur lime rootstock, was first seen in 1999 in Brazil, where it is present in the southern Triângulo Mineiro and northwestern São Paulo State. The disease is a serious threat to the citrus industry, as 85% of 200 million sweet orange trees in the State of São Paulo are grafted on Rangpur lime. After showing general decline symptoms, affected trees suddenly collapse and die, in a manner similar to trees grafted on sour orange rootstock when affected by tristeza decline caused by infection with Citrus tristeza virus (CTV). In tristeza-affected trees, the sour orange bark near the bud union undergoes profound anatomical changes. Light and electron microscopic studies showed very similar changes in the Rangpur lime bark below the bud union of CSD-affected trees: size reduction of phloem cells, collapse and necrosis of sieve tubes, overproduction and degradation of phloem, accumulation of nonfunctioning phloem (NFP), and invasion of the cortex by old NFP. In both diseases, the sweet orange bark near the bud union was also affected by necrosis of sieve tubes, and the phloem parenchyma contained characteristic "chromatic" cells. In CSD-affected trees, these cells were seen not only in the sweet orange phloem, but also in the Rangpur lime phloem. Recent observations indicated that CSD affected not only citrus trees grafted on Rangpur lime but also those on Volkamer lemon, with anatomical symptoms similar to those seen in Rangpur lime bark. Trees on alternative rootstocks, such as Cleopatra mandarin and Swingle citrumelo, showed no symptoms of CSD. CSD-affected trees did recover when they were inarched with seedlings of these rootstocks, but not when inarched with Rangpur lime seedlings. These results indicate that CSD is a bud union disease. In addition, the bark of inarched Rangpur lime and Volkamer lemon seedlings showed, near the approach-graft union, the same anatomical alterations as the bud union bark from the Rangpur lime rootstock in CSD-affected trees. The dsRNA patterns from CSD-affected trees and unaffected trees were similar and indicative of CTV. CSD-affected trees did not react by immunoprinting-ELISA using monoclonal antibodies against 11 viruses. No evidence supported the involvement of viroids in CSD. The potential involvement of CTV and other viruses in CSD is discussed.

The basic reproduction ratio for a model of directly transmitted infections considering the virus charge and the immunological response.

In order to describe mathematically the transmission of microparasites, especially directly transmitted infections, it is usual to set up differential equations assuming the mass action law and a homogeneously mixed population. In this paper we analyze such a model taking into account heterogeneity with respect to the infectivity, that is, the variability in the evolution of the interaction between parasite and the human host during the infectious period. The well established biological phenomenon of initial increase in parasite abundance followed by its decrease, due to the interaction between the host's immunological response and the parasite, has thus been taken into account. The variable amount of microparasites eliminated by an infectious individual, and the different (heterogeneous) immunological response build up by the host when in interaction with parasite are present in the model. The analytical expression for the basic reproduction ratio is derived through stability analysis.

Diffusion model applied to postfeeding larval dispersal blowflies (Diptera: Calliphoridae)

This paper presents a diffusion model of larval dispersal especifically designed to account for particular aspects of postfeeding larval dispersal from the food source in organisms such as blowflies. In these organisms the dispersal of immatures includes two groups of individuals, those that are actively migrating and those that initiated the pupation process. The classical diffusion equation in one dimension was modified to incorporate a function which describes the burying of larvae to become pupae. The analytical solution of this equation predicts oscillatory and monotonic dispersal behaviors, which are observed in experimental populations of blowfly species.

Diffusion model applied to postfeeding larval dispersal in blowflies (Diptera:Calliphoridae).

This paper presents a diffusion model of larval dispersal specifically designed to account for particular aspects of postfeeding larval dispersal from the food source in organisms such as blowflies. In these organisms the dispersal of immatures includes two groups of individuals, those that are actively migrating and those that have initiated the pupation process. The classical diffusion equation in one dimension was modified to incorporate a function which describes the burying of larvae to become pupae. The analytical solution of this equation predicts oscillatory and monotonic dispersal behaviors, which are observed in experimental populations of blowfly species.

Drug kinetics and drug resistance in optimal chemotherapy.

A system of differential equations for the control of tumor cells growth in a cycle nonspecific chemotherapy is presented. First-order drug kinetics and drug resistance are taken into account in a class of optimal control problems. The results show that the strategy corresponding to the maximum rate of drug injection is optimal for the Malthusian model of cell growth (which is a relatively good model for the initial phase of tumor growth). For more general models of cell growth, this strategy proved to be suboptimal under certain conditions.

Chemotherapeutic treatments involving drug resistance and level of normal cells as a criterion of toxicity.

A system of differential equations for the control of tumor cells growth in a cycle nonspecific chemotherapy is presented. Drug resistance and toxicity conveyed through the level of normal cells are taken into account in a class of optimal control problems. Alternative treatments for the exponential tumor growth are set forth for cases where optimal treatments are not available.

Optimal chemotherapy: a case study with drug resistance, saturation effect, and toxicity.

A system of differential equations for the control of tumour cell growth in a cycle-nonspecific chemotherapy is presented. A rate-of-kill term of saturation type, drug resistance, and toxicity are taken into account in a class of optimal control problems. Some results are obtained for general tumour cell growth rates. A detailed analysis is presented for the Malthusian cell growth, which shows a variety of optimal treatments according to the values of the model parameters and initial tumour level.

Optimal chemical control of populations developing drug resistance.

A system of differential equations for the control of the growth of certain populations by the use of chemical treatment is presented. Rather general growth rates and kill rates of drugs, as well as drug resistance, are considered. A class of optimal control problems with a performance criterion depending on a parameter is formulated and shown to admit the same basic optimal strategy. Applications to cycle nonspecific chemotherapy and control of the growth of bacterial populations in cellulose media in paper production plants are described.