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Generalizing the Infectious Disease Model Taking Into Account Diffusion Perturbations, Logistic Dynamics, and Biostimulation

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Abstract

A mathematical model of biinfection is generalized for the conditions of concentrated automated control, taking into account diffusion perturbations, biostimulation, and logistic dynamics of viral elements and antibodies. The solution to the original singularly perturbed problem with a delay is presented as an appropriately adapted stepwise numerically asymptotic approximation procedure. The results of the computer experiments are presented. They demonstrate the peculiarities of the influence of biostimulation and immunotherapy on the development of a chronic disease, taking into account the diffuse “scattering” and logistic population dynamics of viruses and antibodies. It is shown that under conditions of diffusion “scattering,” biostimulation alone is not sufficient to obtain the desired therapeutic effect in a stationary state. It is emphasized that in practical situations of making a decision regarding the treatment of chronic diseases, it is advisable to use a discrete procedure of adaptive automatic control of the immune response with the complex use of biostimulation and immunotherapy.

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Authors and Affiliations

  1. Educational and Scientific Institute of Automatics, Cybernetics, and Computer Engineering of the National University of Water and Environmental Engineering, Rivne, Ukraine

    S. V. Baranovsky & A. Ya. Bomba

Authors
  1. S. V. Baranovsky
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  2. A. Ya. Bomba
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Correspondence to S. V. Baranovsky.

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Translated from Kibernetyka ta Systemnyi Analiz, No. 1, January–February, 2023, pp. 156–168.

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Baranovsky, S.V., Bomba, A.Y. Generalizing the Infectious Disease Model Taking Into Account Diffusion Perturbations, Logistic Dynamics, and Biostimulation. Cybern Syst Anal 59, 134–145 (2023). https://doi.org/10.1007/s10559-023-00549-3

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  • DOI: https://doi.org/10.1007/s10559-023-00549-3

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