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      A Mathematical Model of Intra-Colony Spread of American Foulbrood in European Honeybees ( Apis mellifera L.)

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          Abstract

          American foulbrood (AFB) is one of the severe infectious diseases of European honeybees ( Apis mellifera L.) and other Apis species. This disease is caused by a gram-positive, spore-forming bacterium Paenibacillus larvae. In this paper, a compartmental (SI framework) model is constructed to represent the spread of AFB within a colony. The model is analyzed to determine the long-term fate of the colony once exposed to AFB spores. It was found out that without effective and efficient treatment, AFB infection eventually leads to colony collapse. Furthermore, infection thresholds were predicted based on the stability of the equilibrium states. The number of infected cell combs is one of the factors that drive disease spread. Our results can be used to forecast the transmission timeline of AFB infection and to evaluate the control strategies for minimizing a possible epidemic.

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          American Foulbrood in honeybees and its causative agent, Paenibacillus larvae.

          After more than a century of American Foulbrood (AFB) research, this fatal brood infection is still among the most deleterious bee diseases. Its etiological agent is the Gram-positive, spore-forming bacterium Paenibacillus larvae. Huge progress has been made, especially in the last 20 years, in the understanding of the disease and of the underlying host-pathogen interactions. This review will place these recent developments in the study of American Foulbrood and of P. larvae into the general context of AFB research. Copyright 2009 Elsevier Inc. All rights reserved.
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            Reclassification of Paenibacillus larvae subsp. pulvifaciens and Paenibacillus larvae subsp. larvae as Paenibacillus larvae without subspecies differentiation.

            A polyphasic taxonomic study of the two subspecies of Paenibacillus larvae, Paenibacillus larvae subsp. larvae and Paenibacillus larvae subsp. pulvifaciens, supported the reclassification of the subspecies into one species, Paenibacillus larvae, without subspecies separation. Our conclusions are based on the analysis of six reference strains of P. larvae subsp. pulvifaciens and three reference strains and 44 field isolates of P. larvae. subsp. larvae. The latter originated from brood or honey of clinically diseased honey bee colonies or from honey of both clinically diseased and asymptomatic colonies from Sweden, Finland and Germany. Colony and spore morphology, as well as the metabolism of mannitol and salicin, did not allow a clear identification of the two subspecies and SDS-PAGE of whole-cell proteins did not support the subspecies differentiation. For genomic fingerprinting, repetitive element-PCR fingerprinting using ERIC primers and PFGE of bacterial DNA were performed. The latter method is a high-resolution DNA fingerprinting method proven to be superior to most other methods for biochemical and molecular typing and has not previously been used to characterize P. larvae. ERIC-PCR identified four different genotypes, while PFGE revealed two main clusters. One cluster included most of the P. larvae subsp. larvae field isolates, as well as all P. larvae subsp. pulvifaciens reference strains. The other cluster comprised the pigmented variants of P. larvae subsp. larvae. 16S rRNA gene sequences were determined for some strains. Finally, exposure bioassays demonstrated that reference strains of P. larvae subsp. pulvifaciens were pathogenic for honey bee larvae, producing symptoms similar to reference strains of P. larvae subsp. larvae. In comparison with the type strain for P. larvae subsp. larvae, ATCC 9545T, the P. larvae subsp. pulvifaciens strains tested were even more virulent, since they showed a shorter LT100. An emended description of the species is given.
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              A Quantitative Model of Honey Bee Colony Population Dynamics

              Since 2006 the rate of honey bee colony failure has increased significantly. As an aid to testing hypotheses for the causes of colony failure we have developed a compartment model of honey bee colony population dynamics to explore the impact of different death rates of forager bees on colony growth and development. The model predicts a critical threshold forager death rate beneath which colonies regulate a stable population size. If death rates are sustained higher than this threshold rapid population decline is predicted and colony failure is inevitable. The model also predicts that high forager death rates draw hive bees into the foraging population at much younger ages than normal, which acts to accelerate colony failure. The model suggests that colony failure can be understood in terms of observed principles of honey bee population dynamics, and provides a theoretical framework for experimental investigation of the problem.
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                Author and article information

                Contributors
                Role: Editor
                Journal
                PLoS One
                PLoS ONE
                plos
                plosone
                PLoS ONE
                Public Library of Science (San Francisco, CA USA )
                1932-6203
                2015
                16 December 2015
                : 10
                : 12
                : e0143805
                Affiliations
                [1 ]Institute of Mathematical Sciences and Physics, University of the Philippines Los Baños, Laguna, Philippines
                [2 ]Institute of Biological Sciences, University of the Philippines Los Baños, Laguna, Philippines
                [3 ]UPLB Bee Program, University of the Philippines Los Baños, Laguna, Philippines
                University of Arizona, UNITED STATES
                Author notes

                Competing Interests: The authors have declared that no competing interests exist.

                Conceived and designed the experiments: EOJ JFR ECJ. Performed the experiments: EOJ JFR ECJ CGBB ACF. Analyzed the data: EOJ. Wrote the paper: EOJ JFR ECJ. Served as the lead author: EOJ. Reviewed the manuscript: EOJ JFR ECJ CGBB ACF .

                Article
                PONE-D-15-27969
                10.1371/journal.pone.0143805
                4682658
                26674357
                49ad591b-4f8b-44af-a4f1-a80117a25434
                © 2015 Jatulan et al

                This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited

                History
                : 26 June 2015
                : 10 November 2015
                Page count
                Figures: 11, Tables: 2, Pages: 13
                Funding
                The authors have no support or funding to report.
                Categories
                Research Article
                Custom metadata
                All relevant data are within the paper and its Supporting Information files.

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