On time-discretized versions of the stochastic SIS epidemic model: a comparative analysis

Abstract

This is a repository copy of On time-discretized versions of the stochastic SIS epidemic model: a comparative analysis.

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

“…In this paper, we complement the work of Gómez-Corral and López-García, 15 Section 3.3, which is related to a stochastic version of the deterministic between-host model of Lipsitch et al 11 for antimicrobial resistance in nosocomial pathogens; in a more general context, see the book of Allen 16 for a comprehensive discussion of results on deterministic epidemic models and their stochastic counterparts. In order to further clarify differences between the sensitive and the resistant bacterial strains, our objective here is to characterize the probability law of the exact reproduction number  𝑒𝑥𝑎𝑐𝑡,0 (Artalejo and López-Herrero, 17 Gómez-Corral et al 18 ) by decomposing this number into two random contributions  𝑆 𝑒𝑥𝑎𝑐𝑡,0 and  𝑅 𝑒𝑥𝑎𝑐𝑡,0 that count secondary infections due to the sensitive and the resistant bacteria, respectively. The main features of the exact reproduction number  𝑒𝑥𝑎𝑐𝑡,0 , compared to the basic reproduction number  0 in Ref.…”

“…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 ).…”

“…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 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 ).…”

On First Passage Times in Discrete Skeletons and Uniformized Versions of a Continuous-Time Markov Chain

“…Acknowledgements The authors express their warm appreciation to Prof. Leandro Pardo for valuable discussions on the use of the Hellinger distance during the elaboration of the article [8]. Indeed, the equations ( 3) and (7) in the present work are motivated from the fact that the Hellinger distance between two probability measures requires these measures to be absolutely continuous with respect to a third probability measure.…”