{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,5]],"date-time":"2026-02-05T21:57:47Z","timestamp":1770328667299,"version":"3.49.0"},"reference-count":49,"publisher":"Public Library of Science (PLoS)","issue":"9","license":[{"start":{"date-parts":[[2025,9,24]],"date-time":"2025-09-24T00:00:00Z","timestamp":1758672000000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100000266","name":"Engineering and Physical Sciences Research Council","doi-asserted-by":"publisher","award":["2345914"],"award-info":[{"award-number":["2345914"]}],"id":[{"id":"10.13039\/501100000266","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100000266","name":"Engineering and Physical Sciences Research Council","doi-asserted-by":"publisher","award":["IAA3114"],"award-info":[{"award-number":["IAA3114"]}],"id":[{"id":"10.13039\/501100000266","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["www.ploscompbiol.org"],"crossmark-restriction":false},"short-container-title":["PLoS Comput Biol"],"abstract":"<jats:p>We present a mathematical model of the dynamics of <jats:italic>Bacillus anthracis<\/jats:italic> bacteria within the lymph nodes and blood of a host, following inhalation of an initial dose of spores. We also incorporate the dynamics of protective antigen, which is the binding component of the anthrax toxin produced by the bacteria. The model offers a mechanistic description of the early infection dynamics of inhalational anthrax, while its stochastic nature allows us to study the probabilities of different outcomes (for example, how likely it is that the infection will be cleared for a given inhaled dose of spores) in order to explain dose-response data for inhalational anthrax. The model is calibrated via a Bayesian approach, using <jats:italic>in vivo<\/jats:italic> data from New Zealand white rabbit and guinea pig infection studies, enabling within-host parameters to be estimated. We also leverage incubation-period data from the Sverdlovsk 1979 anthrax outbreak to show that the model can accurately describe human time-to-symptoms data under reasonable parameter regimes. Finally, we derive a simple approximate formula for the probability of symptom onset before time <jats:italic>t<\/jats:italic>, assuming that the number of inhaled spores has a Poisson distribution.<\/jats:p>","DOI":"10.1371\/journal.pcbi.1013439","type":"journal-article","created":{"date-parts":[[2025,9,24]],"date-time":"2025-09-24T17:47:47Z","timestamp":1758736067000},"page":"e1013439","update-policy":"https:\/\/doi.org\/10.1371\/journal.pcbi.corrections_policy","source":"Crossref","is-referenced-by-count":1,"title":["Mechanistic within-host mathematical model of inhalational anthrax"],"prefix":"10.1371","volume":"21","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9119-6568","authenticated-orcid":true,"given":"Bevelynn","family":"Whaler","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Grant","family":"Lythe","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Joseph J.","family":"Gillard","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0142-9162","authenticated-orcid":true,"given":"Thomas R.","family":"Laws","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jonathan","family":"Carruthers","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5962-4211","authenticated-orcid":true,"given":"Thomas","family":"Finnie","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Carmen","family":"Molina-Par\u00eds","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Mart\u00edn","family":"L\u00f3pez-Garc\u00eda","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"340","published-online":{"date-parts":[[2025,9,24]]},"reference":[{"issue":"9","key":"pcbi.1013439.ref001","doi-asserted-by":"crossref","first-page":"405","DOI":"10.1016\/S0966-842X(02)02422-8","article-title":"The alveolar macrophage: the Trojan horse of Bacillus anthracis","volume":"10","author":"C Guidi-Rontani","year":"2002","journal-title":"Trends Microbiol."},{"issue":"1","key":"pcbi.1013439.ref002","doi-asserted-by":"crossref","first-page":"9","DOI":"10.1046\/j.1365-2958.1999.01137.x","article-title":"Germination of Bacillus anthracis spores within alveolar macrophages","volume":"31","author":"C Guidi-Rontani","year":"1999","journal-title":"Mol Microbiol."},{"issue":"9","key":"pcbi.1013439.ref003","doi-asserted-by":"crossref","first-page":"5545","DOI":"10.4049\/jimmunol.174.9.5545","article-title":"Dendritic cells endocytose Bacillus anthracis spores: implications for anthrax pathogenesis","volume":"174","author":"KC Brittingham","year":"2005","journal-title":"J Immunol."},{"issue":"1","key":"pcbi.1013439.ref004","doi-asserted-by":"crossref","first-page":"86","DOI":"10.1086\/504686","article-title":"Resident CD11c+ lung cells are impaired by anthrax toxins after spore infection","volume":"194","author":"A Cleret","year":"2006","journal-title":"J Infect Dis."},{"issue":"12","key":"pcbi.1013439.ref005","doi-asserted-by":"crossref","first-page":"7994","DOI":"10.4049\/jimmunol.178.12.7994","article-title":"Lung dendritic cells rapidly mediate anthrax spore entry through the pulmonary route.","volume":"178","author":"A Cleret","year":"2007","journal-title":"J Immunol."},{"issue":"6","key":"pcbi.1013439.ref006","doi-asserted-by":"crossref","first-page":"453","DOI":"10.1046\/j.1462-5822.2000.00067.x","article-title":"Early bacillus anthracis-macrophage interactions: intracellular survival survival and escape","volume":"2","author":"TC Dixon","year":"2000","journal-title":"Cell Microbiol."},{"issue":"2","key":"pcbi.1013439.ref007","doi-asserted-by":"crossref","first-page":"701","DOI":"10.1016\/S0002-9440(10)63697-8","article-title":"Pathology and pathogenesis of bioterrorism-related inhalational anthrax","volume":"163","author":"J Guarner","year":"2003","journal-title":"Am J Pathol."},{"key":"pcbi.1013439.ref008","doi-asserted-by":"crossref","first-page":"185","DOI":"10.1146\/annurev-micro-091014-104523","article-title":"Anthrax pathogenesis","volume":"69","author":"M Moayeri","year":"2015","journal-title":"Annu Rev Microbiol."},{"issue":"8","key":"pcbi.1013439.ref009","doi-asserted-by":"crossref","first-page":"1173","DOI":"10.1111\/j.1462-5822.2005.00545.x","article-title":"Anthrax toxin receptor 2 mediates Bacillus anthracis killing of macrophages following spore challenge","volume":"7","author":"DJ Banks","year":"2005","journal-title":"Cell Microbiol."},{"key":"pcbi.1013439.ref010","doi-asserted-by":"crossref","first-page":"1146","DOI":"10.1016\/j.micinf.2011.07.005","article-title":"Key aspects of the molecular and cellular basis of inhalational anthrax","volume":"13","author":"CK Cote","year":"2011","journal-title":"Microbes and Infection."},{"issue":"1","key":"pcbi.1013439.ref011","doi-asserted-by":"crossref","first-page":"20","DOI":"10.12998\/wjcc.v3.i1.20","article-title":"Anthrax: A disease of biowarfare and public health importance","volume":"3","author":"AK Goel","year":"2015","journal-title":"World J Clin Cases."},{"issue":"4","key":"pcbi.1013439.ref012","doi-asserted-by":"crossref","first-page":"531","DOI":"10.1002\/sim.2033","article-title":"Modelling the incubation period of anthrax","volume":"24","author":"R Brookmeyer","year":"2005","journal-title":"Stat Med."},{"key":"pcbi.1013439.ref013","doi-asserted-by":"crossref","first-page":"2","DOI":"10.3389\/fcimb.2018.00002","article-title":"Innate Immune Interactions between Bacillus anthracis and Host Neutrophils","volume":"8","author":"JZ Liu","year":"2018","journal-title":"Front Cell Infect Microbiol."},{"key":"pcbi.1013439.ref014","first-page":"2865","article-title":"A stochastic intracellular model of anthrax infection with spore germination heterogeneity","author":"B Williams","year":"2021","journal-title":"Front Immunol."},{"key":"pcbi.1013439.ref015","doi-asserted-by":"crossref","first-page":"18","DOI":"10.1016\/j.mbs.2018.08.010","article-title":"Modeling the macrophage-anthrax spore interaction: Implications for early host-pathogen interactions","volume":"305","author":"B Pantha","year":"2018","journal-title":"Math Biosci."},{"issue":"1","key":"pcbi.1013439.ref016","doi-asserted-by":"crossref","first-page":"199","DOI":"10.1016\/j.jtbi.2011.01.054","article-title":"Modeling the host response to inhalation anthrax","volume":"276","author":"J Day","year":"2011","journal-title":"J Theor Biol."},{"issue":"1","key":"pcbi.1013439.ref017","doi-asserted-by":"crossref","first-page":"29","DOI":"10.1089\/bsp.2013.0067","article-title":"Deterministic models of inhalational anthrax in New Zealand white rabbits","volume":"12","author":"B Gutting","year":"2014","journal-title":"Biosecur Bioterror."},{"key":"pcbi.1013439.ref018","doi-asserted-by":"crossref","first-page":"1165","DOI":"10.3389\/fmicb.2018.01165","article-title":"A novel stochastic multi-scale model of Francisella tularensis infection to predict risk of infection in a laboratory","volume":"9","author":"J Carruthers","year":"2018","journal-title":"Frontiers in Microbiology."},{"key":"pcbi.1013439.ref019","doi-asserted-by":"crossref","unstructured":"Abramova FA, Grinberg LM, Yampolskaya OV, Walker DH. Pathology of inhalational anthrax in 42 cases from the Sverdlovsk outbreak of 1979. Proceedings of the National Academy of Sciences. 1993;90(6):2291\u20134.","DOI":"10.1073\/pnas.90.6.2291"},{"issue":"1","key":"pcbi.1013439.ref020","doi-asserted-by":"crossref","first-page":"469","DOI":"10.1128\/IAI.74.1.469-480.2006","article-title":"Roles of macrophages and neutrophils in the early host response tobacillus anthracisspores in a mouse model of infection","volume":"74","author":"CK Cote","year":"2006","journal-title":"Infect Immun."},{"issue":"5","key":"pcbi.1013439.ref021","doi-asserted-by":"crossref","first-page":"811","DOI":"10.1111\/risa.12326","article-title":"Evaluation of inhaled versus deposited dose using the exponential dose-response model for inhalational anthrax in nonhuman primate, rabbit, and guinea pig","volume":"35","author":"BW Gutting","year":"2015","journal-title":"Risk Anal."},{"key":"pcbi.1013439.ref022","doi-asserted-by":"crossref","first-page":"87","DOI":"10.3389\/fcimb.2012.00087","article-title":"Inhalational anthrax (Ames aerosol) in na\u00efve and vaccinated New Zealand rabbits: characterizing the spread of bacteria from lung deposition to bacteremia","volume":"2","author":"BW Gutting","year":"2012","journal-title":"Front Cell Infect Microbiol."},{"issue":"4","key":"pcbi.1013439.ref023","doi-asserted-by":"crossref","first-page":"1152","DOI":"10.1128\/IAI.01289-12","article-title":"Pathology and pathophysiology of inhalational anthrax in a guinea pig model","volume":"81","author":"V Savransky","year":"2013","journal-title":"Infect Immun."},{"issue":"31","key":"pcbi.1013439.ref024","doi-asserted-by":"crossref","first-page":"187","DOI":"10.1098\/rsif.2008.0172","article-title":"Approximate Bayesian computation scheme for parameter inference and model selection in dynamical systems","volume":"6","author":"T Toni","year":"2009","journal-title":"J R Soc Interface."},{"issue":"8","key":"pcbi.1013439.ref025","article-title":"Quantitative models of the dose-response and time course of inhalational anthrax in humans","volume":"9","author":"DJA Toth","year":"2013","journal-title":"PLoS Pathog."},{"issue":"1","key":"pcbi.1013439.ref026","doi-asserted-by":"crossref","first-page":"33","DOI":"10.1038\/s41540-024-00357-1","article-title":"Quantifying in vitro B. anthracis growth and PA production and decay: a mathematical modelling approach","volume":"10","author":"B Williams","year":"2024","journal-title":"NPJ Syst Biol Appl."},{"issue":"3","key":"pcbi.1013439.ref027","doi-asserted-by":"crossref","first-page":"236","DOI":"10.1016\/0273-2300(87)90036-5","article-title":"Feasibility of dose adjustment based on differences in long-term clearance rates of inhaled particulate matter in humans and laboratory animals","volume":"7","author":"WE Pepelko","year":"1987","journal-title":"Regul Toxicol Pharmacol."},{"issue":"3","key":"pcbi.1013439.ref028","doi-asserted-by":"crossref","first-page":"56","DOI":"10.3390\/toxins8030056","article-title":"Quantitative Determination of lethal toxin proteins in culture supernatant of human live anthrax vaccine bacillus anthracis A16R","volume":"8","author":"X Zai","year":"2016","journal-title":"Toxins (Basel)."},{"issue":"5","key":"pcbi.1013439.ref029","doi-asserted-by":"crossref","first-page":"1453","DOI":"10.1111\/j.1365-2672.2007.03391.x","article-title":"A study of the physiology of Bacillus anthracis Sterne during manufacture of the UK acellular anthrax vaccine","volume":"103","author":"S Charlton","year":"2007","journal-title":"J Appl Microbiol."},{"key":"pcbi.1013439.ref030","volume-title":"Prepositioning antibiotics for anthrax","author":"RR Bass","year":"2012"},{"issue":"20","key":"pcbi.1013439.ref031","doi-asserted-by":"crossref","first-page":"7589","DOI":"10.1073\/pnas.0509551103","article-title":"Sverdlovsk revisited: modeling human inhalation anthrax","volume":"103","author":"DA Wilkening","year":"2006","journal-title":"Proc Natl Acad Sci U S A."},{"issue":"4","key":"pcbi.1013439.ref032","doi-asserted-by":"crossref","first-page":"593","DOI":"10.1177\/0272989X08315245","article-title":"Modeling the incubation period of inhalational anthrax","volume":"28","author":"DA Wilkening","year":"2008","journal-title":"Med Decis Making."},{"issue":"1","key":"pcbi.1013439.ref033","doi-asserted-by":"crossref","first-page":"28","DOI":"10.1017\/S0022172400044272","article-title":"Observations on the prophylaxis of experimental pulmonary anthrax in the monkey","volume":"54","author":"DW HENDERSON","year":"1956","journal-title":"J Hyg (Lond)."},{"key":"pcbi.1013439.ref034","unstructured":"Asgharian B, Price O, Miller F, Subramaniam R, Cassee F, Freijer J, et al. Multiple-path particle dosimetry model (MPPD v 2.11): a model for human and rat airway particle dosimetry. Hamner Institutes for Health Sciences Applied Research Associates (ARA), National Institute for Public Health and the Environment (RIVM), and Ministry of Housing, Spatial Planning and the Environment, Editor. 2009."},{"issue":"1","key":"pcbi.1013439.ref035","doi-asserted-by":"crossref","first-page":"218","DOI":"10.1111\/j.1365-2958.2010.07335.x","article-title":"Reversal of an epigenetic switch governing cell chaining in Bacillus subtilis by protein instability","volume":"78","author":"Y Chai","year":"2010","journal-title":"Mol Microbiol."},{"key":"pcbi.1013439.ref036","first-page":"2020","article-title":"Bacillus anthracis chain length, a virulence determinant, is regulated by a transmembrane Ser\/Thr protein kinase PrkC","author":"N Dhasmana","year":"2020","journal-title":"bioRxiv."},{"issue":"11","key":"pcbi.1013439.ref037","doi-asserted-by":"crossref","first-page":"7495","DOI":"10.1128\/IAI.73.11.7495-7501.2005","article-title":"Murine macrophages kill the vegetative form of Bacillus anthracis","volume":"73","author":"TJ Kang","year":"2005","journal-title":"Infect Immun."},{"key":"pcbi.1013439.ref038","doi-asserted-by":"crossref","first-page":"30","DOI":"10.1016\/j.epidem.2017.06.001","article-title":"A human time dose response model for Q fever","volume":"21","author":"CW Heppell","year":"2017","journal-title":"Epidemics."},{"issue":"6","key":"pcbi.1013439.ref039","doi-asserted-by":"crossref","first-page":"2689","DOI":"10.1128\/IAI.01875-06","article-title":"Murine aerosol challenge model of anthrax","volume":"75","author":"CL Loving","year":"2007","journal-title":"Infect Immun."},{"key":"pcbi.1013439.ref040","doi-asserted-by":"crossref","DOI":"10.1093\/cid\/ciac534","article-title":"Clinical Features of Patients Hospitalized for All Routes of Anthrax 1880 -2018: A Systematic Review","volume":"75","author":"K Hendricks","year":"2022","journal-title":"Clin Infect Dis."},{"issue":"1","key":"pcbi.1013439.ref041","doi-asserted-by":"crossref","first-page":"2","DOI":"10.1111\/j.1600-0668.2009.00621.x","article-title":"Review and comparison between the Wells-Riley and dose-response approaches to risk assessment of infectious respiratory diseases","volume":"20","author":"GN Sze To","year":"2010","journal-title":"Indoor Air."},{"issue":"2","key":"pcbi.1013439.ref042","doi-asserted-by":"crossref","DOI":"10.1111\/ina.12976","article-title":"Modeling the factors that influence exposure to SARS-CoV-2 on a subway train carriage","volume":"32","author":"D Miller","year":"2022","journal-title":"Indoor Air."},{"key":"pcbi.1013439.ref043","doi-asserted-by":"crossref","first-page":"101829","DOI":"10.1016\/j.jth.2024.101829","article-title":"A quantitative microbial risk assessment approach to estimate exposure to SARS-CoV-2 on a bus","volume":"38","author":"AM Bate","year":"2024","journal-title":"J Transport Health."},{"key":"pcbi.1013439.ref044","doi-asserted-by":"crossref","first-page":"216","DOI":"10.1186\/s12866-016-0838-9","article-title":"Time-kill curve analysis and pharmacodynamic modelling for in vitro evaluation of antimicrobials against Neisseria gonorrhoeae","volume":"16","author":"S Foerster","year":"2016","journal-title":"BMC Microbiol."},{"issue":"13","key":"pcbi.1013439.ref045","doi-asserted-by":"crossref","first-page":"5828","DOI":"10.1021\/es200901e","article-title":"A model for in-vivo delivered dose estimation for inhaled bacillus anthracis spores in humans with interspecies extrapolation","volume":"45","author":"MH Weir","year":"2011","journal-title":"Environ Sci Technol."},{"issue":"1","key":"pcbi.1013439.ref046","doi-asserted-by":"crossref","first-page":"67","DOI":"10.1111\/risa.13597","article-title":"Dose\u2013response modeling: extrapolating from experimental data to real-world populations","volume":"41","author":"A Pratt","year":"2020","journal-title":"Risk Analysis."},{"key":"pcbi.1013439.ref047","doi-asserted-by":"crossref","first-page":"35","DOI":"10.1146\/annurev.physchem.58.032806.104637","article-title":"Stochastic simulation of chemical kinetics","volume":"58","author":"DT Gillespie","year":"2007","journal-title":"Annu Rev Phys Chem."},{"issue":"6","key":"pcbi.1013439.ref048","doi-asserted-by":"crossref","first-page":"207","DOI":"10.1038\/laban.787","article-title":"Blood collection in the guinea pig (Cavia porcellus)","volume":"44","author":"WR Williams","year":"2015","journal-title":"Lab Anim."},{"issue":"2","key":"pcbi.1013439.ref049","doi-asserted-by":"crossref","first-page":"276","DOI":"10.1111\/j.1365-2672.2012.05314.x","article-title":"Effect of animal sera on Bacillus anthracis Sterne spore germination and vegetative cell growth","volume":"113","author":"MD Bensman","year":"2012","journal-title":"J Appl Microbiol."}],"container-title":["PLOS Computational Biology"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dx.plos.org\/10.1371\/journal.pcbi.1013439","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,9,24]],"date-time":"2025-09-24T17:47:56Z","timestamp":1758736076000},"score":1,"resource":{"primary":{"URL":"https:\/\/dx.plos.org\/10.1371\/journal.pcbi.1013439"}},"subtitle":[],"editor":[{"given":"Brittany","family":"Rife Magalis","sequence":"first","affiliation":[],"role":[{"role":"editor","vocabulary":"crossref"}]}],"short-title":[],"issued":{"date-parts":[[2025,9,24]]},"references-count":49,"journal-issue":{"issue":"9","published-online":{"date-parts":[[2025,9,24]]}},"URL":"https:\/\/doi.org\/10.1371\/journal.pcbi.1013439","relation":{},"ISSN":["1553-7358"],"issn-type":[{"value":"1553-7358","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,9,24]]}}}