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

Autor: Lena-Maria Pfurtscheller, Jhoana P. Romero-Leiton, Hermann Mena
Rok vydání: 2020
Předmět:
Work (thermodynamics)
Stochastic modelling
Control variable
02 engineering and technology
deterministic model
Stability (probability)
antibiotics
Quantitative Biology::Cell Behavior
Antibiotic resistance
sensitive bacteria
resistant bacteria
0502 economics and business
QA1-939
0202 electrical engineering
electronic engineering
information engineering
Humans
Applied mathematics
stochastic model
Mathematics
Stochastic Processes
Bacteria
Applied Mathematics
05 social sciences
Bacterial Infections
General Medicine
Models
Theoretical
stability
Optimal control
Anti-Bacterial Agents
Computational Mathematics
Resistant bacteria
Distribution (mathematics)
optimal control problem
Modeling and Simulation
020201 artificial intelligence & image processing
General Agricultural and Biological Sciences
equilibrium solutions
TP248.13-248.65
050203 business & management
Biotechnology
Zdroj: Mathematical Biosciences and Engineering, Vol 17, Iss 5, Pp 4477-4499 (2020)
ISSN: 1551-0018
Popis: In this work, we study a mathematical model for the interaction of sensitive-resistant bacteria to antibiotics and analyse the effects of introducing random perturbations to this model. We compare the results of existence and stability of equilibrium solutions between the deterministic and stochastic formulations, and show that the conditions for the bacteria to die out are weaker in the stochastic model. Moreover, a corresponding optimal control problem is formulated for the unperturbed and the perturbed system, where the control variable is prophylaxis. The results of the optimal control problem reveal that, depending on the antibiotics, the costs of the prophylaxis, such as implementation, ordering and distribution, have to be much lower than the social costs, to achieve a bacterial resistance effective control.
Databáze: OpenAIRE
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