Random perturbations in a mathematical model of bacterial resistance: Analysis and optimal control

Mena, Hermann; Pfurtscheller, Lena-Maria; Romero–Leiton, Jhoana P.

doi:10.3934/mbe.2020247

Cited by 8 publications

(3 citation statements)

References 34 publications

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“…The study found that government intervention and authoritative media reports would interfere with the influence Internet users’ opinions, thereby preventing the spread of Internet users, thus suppressing the rumor spreading rumors. Additionally, Mena et al(2020) and Zhou et al(2022) analyzed the extinction and persistence of the uncertain dissemination model, and further analyzed the characteristics of dissemination by constructing the optimal control model [ 40 , 41 ].…”

Section: Introductionmentioning

confidence: 99%

Dynamic analysis and optimal control of stochastic information cross-dissemination and variation model with random parametric perturbations

Kang,

Liu,

Liu

et al. 2024

PLoS ONE

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Information dissemination has a significant impact on social development. This paper considers that there are many stochastic factors in the social system, which will result in the phenomena of information cross-dissemination and variation. The dual-system stochastic susceptible-infectious-mutant-recovered model of information cross-dissemination and variation is derived from this problem. Afterward, the existence of the global positive solution is demonstrated, sufficient conditions for the disappearance of information and its stationary distribution are calculated, and the optimal control strategy for the stochastic model is proposed. The numerical simulation supports the results of the theoretical analysis and is compared to the parameter variation of the deterministic model. The results demonstrate that cross-dissemination of information can result in information variation and diffusion. Meanwhile, white noise has a positive effect on information dissemination, which can be improved by adjusting the perturbation parameters.

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Section: Introductionmentioning

confidence: 99%

Dynamic analysis and optimal control of stochastic information cross-dissemination and variation model with random parametric perturbations

Kang,

Liu,

Liu

et al. 2024

PLoS ONE

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“…Huo and Dong [32] developed a stochastic ISR model with white noise media coverage, and the results of their study demonstrated that media coverage was inversely proportional to rumor spread. In addition, Mena et al [33] analyzed the spread characteristics by developing an optimal control model based on the analysis of extinction and persistence of uncertain spread models.…”

Section: Introductionmentioning

confidence: 99%

Dynamic analysis and optimal control of a stochastic information spreading model considering super-spreader and implicit exposer with random parametric perturbations

Kang

Hou

et al. 2023

Front. Phys.

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Environmental factors in social systems affect information spreading at all times. This paper proposes a stochastic S2EIR model that considers the presence of super-spreaders and implicit exposers in information spreading, as well as the stochastic perturbation of model parameters. The existence of a global positive solution using the Itô′s formula is then demonstrated. Sufficient conditions for information disappearance and smooth distribution of information are calculated by using the Borel–Cantelli lemma and the strong law of large numbers. Furthermore, the optimal control strategy for the stochastic model is proposed using the Hamiltonian function. The results of the theoretical analysis are supported by numerical simulations and compared to the parameter variations of the deterministic model. The results of this study indicate that white noise facilitates the spread of information. The intensity of perturbation is proportional to the fluctuation of information spreading. Controlling random parameters can effectively facilitate the spread of information. For positive information, the randomness and complexity of the social system should be utilized to increase the spread of information. In contrast, for negative information, randomness in the social system should be suppressed to the greatest extent possible to limit information dissemination.

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“…La práctica más extendida en el modelado de AMR consiste en clasificar la población en dos estados opuestos; sensibilidad (el antimicrobiano ejerce el máximo efecto inhibitorio) y resistencia (el antimicrobiano no tiene efecto alguno). Estos modelos incluyen además mecanismos biológicos con distintos grados de complejidad, como competencia entre bacterias (Fujikawa et al, 2014) o transferencia horizontal de AMR (Hernández-Beltrán et al, 2021;Zhong et al, 2010), por ejemplo, así como alguna variable o parámetro de naturaleza estocástica (Mena et al, 2020;Gothwal and Thatikonda, 2020). Sin embargo, aunque esta simplificación de la distribución real de resistencia resulta bastante flexible y eficiente en gran variedad de aplicaciones, el ignorar la heterroresistencia inherente a la población puede conducir a graves desviaciones entre el comportamiento real y la predicción arrojada por el modelo.…”

Section: Introductionunclassified

Modelado matemático de heterorresistencia en poblaciones bacterianas sometidas a estrés antimicrobiano

Martínez-López,

Pedreira,

Vilas

et al. 2023

XLIV Jornadas De Automática: Libro De Actas: Universidad De Zaragoza, Escuela De Ingeniería Y Arquitectura, 6, 7 Y 8 De Septiem

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El rápido avance de la resistencia bacteriana a los antimicrobianos continúa fomentando la investigación en torno al modelado matemático de los mecanismos que conducen a la emergencia, transmisión y selección de resistencia. El enfoque más extendido para explicar las dinámicas de una población tratada con antimicrobiano consiste en clasificar las bacterias en sensibles y resistentes. Sin embargo, en la realidad existen infinidad de grados de resistencia intermedios en la población, lo que se conoce como heterorresistencia. En este trabajo, se propone un modelo matemático para explicar las dinámicas de una población heterorresistente, introduciendo el grado de resistencia como una variable aleatoria indicadora de la efectividad del antimicrobiano sobre la población. Se analizan las capacidades del modelo y se establecen, además, su observabilidad e identificabilidad estructurales.

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Random perturbations in a mathematical model of bacterial resistance: Analysis and optimal control

Cited by 8 publications

References 34 publications

Dynamic analysis and optimal control of stochastic information cross-dissemination and variation model with random parametric perturbations

Dynamic analysis and optimal control of stochastic information cross-dissemination and variation model with random parametric perturbations

Dynamic analysis and optimal control of a stochastic information spreading model considering super-spreader and implicit exposer with random parametric perturbations

Modelado matemático de heterorresistencia en poblaciones bacterianas sometidas a estrés antimicrobiano

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