Measures to assess a warning vaccination level in a stochastic SIV model with imperfect vaccine

Gamboa, María; Lopez-Herrero, M. J.

doi:10.1111/sapm.12479

Cited by 6 publications

(2 citation statements)

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“…See, for example, the papers by De Nitto Personè and Grassi, 19 Gaver et al, 20 and Gómez-Corral et al 21 for a detailed discussion on LD-QBD processes and their applications in the context of varicella-zoster virus infections. The work to be presented here is part of our ongoing study on the use of Markov chains, including LD-QBD processes, and related matrix-analytic methods in a variety of stochastic epidemic models, such as SIS and SIR models with two strains and cross-immunity (Almaraz and Gómez-Corral, 22 Amador et al 23 ), discrete and continuous versions of SIS models (Chalub and Sousa, 24 Gómez-Corral et al 25 ), quarantine of hosts (Amador and Gómez-Corral 26 ), limited resources in epidemics (Amador and López-Herrero 27 ), and vaccination strategies (Fernández-Peralta and Gómez-Corral, 28 Gamboa and López-Herrero 29 ).…”

Section: Introductionmentioning

confidence: 99%

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

Chalub,

Gómez‐Corral,

López‐García

et al. 2023

Stud Appl Math

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Ordinary differential equation models used in mathematical epidemiology assume explicitly or implicitly large populations. For the study of infections in a hospital, this is an extremely restrictive assumption as typically a hospital ward has a few dozen, or even fewer, patients. This work reframes a well‐known model used in the study of the spread of antibiotic‐resistant bacteria in hospitals, to consider the pathogen transmission dynamics in small populations. In this vein, this 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. We determine the probability law of the exact reproduction number , 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 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. This guarantees the compatibility of the new, finite‐population model, with large population models present in the literature and takes full advantage, in its mathematical analysis, of the intrinsic stochasticity.

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Section: Introductionmentioning

confidence: 99%

“…), discrete and continuous versions of SIS models (Chalub and Sousa, 24 Gómez‐Corral et al 25 26 ), limited resources in epidemics (Amador and López‐Herrero 27 ), and vaccination strategies (Fernández‐Peralta and Gómez‐Corral, 28 Gamboa and López‐Herrero 29 ).…”

Section: Introductionmentioning

confidence: 99%