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A Markov chain model to investigate the spread of antibiotic-resistant bacteria in hospitals

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dc.contributor.authorChalub, Fabio A.C.C.
dc.contributor.authorGómez-Corral, Antonio
dc.contributor.authorLópez-García, Martín
dc.contributor.authorPalacios-Rodríguez, Fátima
dc.date.accessioned2023-06-22T11:26:52Z
dc.date.available2023-06-22T11:26:52Z
dc.date.issued2023-05-24
dc.description.abstractThis paper proposes a Markov chain model to describe the spread of a single bacterial species in a hospital ward where patients may be free of bacteria or may carry bacterial strains that are either sensitive or resistant to antimicrobial agents. The aim is to determine the probability law of the exact reproduction number Rexact,0 which is here defined as the random number of secondary infections generated by those patients who are accommodated in a predetermined bed before a patient who is free of bacteria is accommodated in this bed for the first time. Specifically, we decompose the exact reproduction number Rexact,0 into two contributions allowing us to distinguish between infections due to the sensitive and the resistant bacterial strains. Our methodology is mainly based on structured Markov chains and the use of related matrix-analytic methods.
dc.description.departmentDepto. de Estadística e Investigación Operativa
dc.description.facultyFac. de Ciencias Matemáticas
dc.description.refereedFALSE
dc.description.sponsorshipMinisterio de Ciencia e Innovación
dc.description.sponsorshipFundação para a Ciência e a Tecnologia (Portugal)
dc.description.statusunpub
dc.eprint.idhttps://eprints.ucm.es/id/eprint/78823
dc.identifier.urihttps://hdl.handle.net/20.500.14352/72422
dc.language.isoeng
dc.relation.projectIDPGC2018-097704-B-I00
dc.relation.projectIDUID/MAT/00297/2019; UIDB/00297/2020; 2022.03091.PTDC
dc.rightsAtribución 3.0 España
dc.rights.accessRightsopen access
dc.rights.urihttps://creativecommons.org/licenses/by/3.0/es/
dc.subject.cdu519.217
dc.subject.keywordEpidemic model
dc.subject.keywordMarkov chain
dc.subject.keywordQuasi-birth-death process
dc.subject.keywordReproduction number
dc.subject.ucmInvestigación operativa (Matemáticas)
dc.subject.ucmProcesos estocásticos
dc.subject.ucmBiomatemáticas
dc.subject.unesco1207 Investigación Operativa
dc.subject.unesco1208.08 Procesos Estocásticos
dc.subject.unesco2404 Biomatemáticas
dc.titleA Markov chain model to investigate the spread of antibiotic-resistant bacteria in hospitals
dc.typejournal article
dcterms.references[1] Allen LJS (2003) An Introduction to Stochastic Processes with Applications to Biology. Pearson Education, Inc., Upper Saddle River, NJ. [2] Almaraz E, Gómez-Corral A (2019) Number of infections suffered by a local individual in a two-strain SIS model with partial cross-immunity. Mathematical Methods in the Applied Sciences 42: 4318–4330. [3] Amador J, López-Herrero MJ (2018) Cumulative and maximum epidemic sizes for a nonlinear SEIR stochastic model with limited resources. Discrete and Continuous Dynamical Systems–Series B 23: 3137–3151. [4] Amador J, Armesto D, Gómez-Corral A (2019) Extreme values in SIR epidemic models with two strains and cross–immunity. Mathematical Biosciences and Engineering 16: 1992–2022. [5] Amador J, Gómez-Corral A (2020) A stochastic model with two quarantine states and a limited carrying capacity for quarantine. Physica A 544: 121899. [6] Artalejo JR, López-Herrero MJ (2013) On the exact measure of disease spread in stochastic epidemic models. Bulletin of Mathematical Biology 75: 1031–1050. [7] Bagkur C, Guler E, Kaymakamzade B, Hincal E, Suer K (2022) Near future perspective of ESBL-producing Klebsiella pneumoniae strains using mathematical modeling. Computer Modeling in Engineering & Sciences 130: 111–132. [8] Breijyeh Z, Jubeh B, Karaman R (2020) Resistance of Gram-negative bacteria to current antibacterial agents and approaches to resolve it. Molecules 25: 1340. [9] Chalub FACC, Souza MO (2009) From discrete to continuous evolution models: A unifying approach to drift-diffusion and replicator dynamics. Theoretical Population Biology 76: 268–277. [10] Chalub FACC, Souza, MO (2011) The SIR epidemic model from a PDE point of view. Mathematical and Computer Modelling 53: 1568–1574. [11] Chalub FACC, Souza MO (2014) Discrete and continuous SIS epidemic models: A unifying approach. Ecological Complexity 18: 83–95. [12] Chalub FACC, Souza MO (2014) The frequency-dependent Wright-Fisher model: Diffusive and non-diffusive approximations. Journal of Mathematical Biology 68: 1089–1133. [13] Chugunova M, Taranets R, Vasylyeva N (2023) Initial-boundary value problems for conservative Kimura-type equations: Solvability, asymptotic and conservation law. Journal of Evolution Equations 23: 17. [14] D’Agata EMC, Horn MA, Webb GF (2002) The impact of persistent gastrointestinal colonization on the transmission dynamics of vancomycin-resistant Enterococci. Journal of Infectious Diseases 185: 766–773. [15] D’Agata EMC, Magal P, Olivier D, Ruan S, Webb GF (2007) Modeling antibiotic resistance in hospitals: The impact of minimizing treatment duration. Journal of Theoretical Biology 249: 487–499. [16] Danilkina O, Souza MO, Chalub FACC (2018) Conservative parabolic problems: Non-degenerated theory and degenerated examples from population dynamics. Mathematical Methods in the Applied Sciences 41: 4391–4406. [17] De Nitto Personè V, Grassi V (1996) Solution of finite QBD processes. Journal of Applied Probability 33: 1003–1010. [18] Fernández-Peralta R, Gómez-Corral A (2021) A structured Markov chain model to investigate the effects of pre-exposure vaccines in tuberculosis control. Journal of Theoretical Biology 509: 110490. [19] Gamboa M, López-Herrero MJ (2022) Measures to asses a warning vaccination level in a stochastic SIV model with imperfect vaccine. Studies in Applied Mathematics 148: 1411-1438. [20] Gaver DP, Jacobs PA, Latouche G (1984) Finite birth-and-death models in randomly changing environments. Advances in Applied Probability 16: 715–731. [21] Gómez-Corral A, López-García M (2018) Perturbation analysis in finite LD-QBD processes and applications to epidemic models. Numerical Linear Algebra with Applications 25: e2160. [22] Gómez-Corral A, López-García M, López-Herrero MJ, Taipe D (2020) On firt-passage times and sojourn times in finite QBD processes and their applications in epidemics. Mathematics 8: 1718. [23] Gómez-Corral A, López-García M, Rodríguez-Bernal MT (2021) On time-discretized versions of SIS epidemic models: A comparative analysis. Journal of Mathematical Biology 82: 46. [24] Gómez-Corral A, Palacios-Rodríguez F, Rodríguez-Bernal MT (2022) On the distribution of the exact reproduction number in SIS epidemic models with vertical transmission. Under review. [25] Gygli SM, Borrell S, Trauner A, Gagneux S (2017) Antimicrobial resistance in Mycobacterium tuberculosis: mechanistic and evolutionary perspectives. FEMS Microbiology Reviews 41: 354–373. [26] Haaber J, Penades JR, Ingmer H (2017) Transfer of antibiotic resistance in Staphylococcus aureus. Trends in Microbiology 25: 327–337. [27] Lipsitch M, Bergstrom CT, Levin BR (2000) The epidemiology of antibiotic resistance in hospitals: Paradoxes and prescriptions. Proceedings of the National Academic of Sciences 976: 1938–1943. [28] Miller WR, Munita JM, Arias CA (2014) Mechanisms of antibiotic resistance in enterococci. Expert Review of Anti-infective Theraphy 12: 1221–1236. [29] Murray CJL, Ikuta KS, Sharara F, Swetschinski L, Robles Aguilar G et al. (2022) Global burden of bacterial antimicrobial resistance in 2019: A systematic analysis. The Lancet 399: 629–655, [30] Niewiadomska AM, Jayabalasingham B, Seidman JC, Willem L, Grenfell B, Spiro D, Voboud C (2019) Population-level mathematical modeling of antimicrobial resistance: A systematic review. BMC Medicine 17: 81. [31] Seigal A, Mira P, Sturmfels B, Barlow M (2017) Does antibiotic resistance evolve in hospitals? Bulletin of Mathematical Biology 79: 191–208. [32] Spicknall IH, Foxman B, Marrs CF, Eisenberg JNS (2013) A modeling framework for the evolution and spread of antibiotiv resistance: Literature review and model categorization. American Journal of Epidemiology 178: 508–520. [33] Techitnutsarut P, Chamchod F (2021) Modeling bacterial resistance to antibiotics: Bacterial conjugation and drug effects. Advances in Difference Equations 2021: 290. [34] Webb GF, D’Agata EMC, Magal P, Ruan S (2005) A model of antibiotic-resistant bacterial epidemics in hospitals. Proceedings of the National Academic of Sciences 102: 13343–13348.
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