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

1 Escuela de Ciencias Matemáticas y Computacionales, Universidad de Investigación de Tecnología Experimental Yachay, Ecuador
2 Institut fur Mathematik, Universität Innsbruck, Austria

Special Issues: Understanding biology with mathematics and simulations

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.
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Keywords sensitive bacteria; resistant bacteria; antibiotics; deterministic model; stochastic model; equilibrium solutions; stability; optimal control problem

Citation: Hermann Mena, Lena-Maria Pfurtscheller, Jhoana P. Romero-Leiton. Random perturbations in a mathematical model of bacterial resistance: Analysis and optimal control. Mathematical Biosciences and Engineering, 2020, 17(5): 4477-4499. doi: 10.3934/mbe.2020247

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