Baranovsky S.V., Bomba A.Y.
Generalizing the infectious disease model taking into account diffusion perturbations, logistics dynamics, and biostimulation

A mathematical model of the dynamics of a viral infection under the conditions of adsorption therapy, taking into account diffusion perturbations, was formed by generalizing the basic model of an infectious disease using the ideas of modeling adsorption mass transfer processes and perturbation theory. Based on the synthesis of a step-by-step procedure, and asymptotic and numerical methods, a computing technology is proposed that provides a stepwise approximation of the solution to a model singularly perturbed problem with a delay as a perturbation of the solution to the corresponding degenerate problem without a delay. The results of the computer modeling illustrate the predictive contribution of the adsorption therapy to the process of neutralization of viral elements in the body. It is noted that the efficiency of the adsorbents is determined, in particular, by the time of their introduction, which is important to consider when making a decision on the use of appropriate additional therapy in the treatment program. © 2023, Springer Science+Business Media, LLC, part of Springer Nature.

Keywords: asymptotic methods, concentrated influences, dynamic systems with delay, infectious disease model, singularly perturbed problems, sorption therapy, Computation theory, Disease control, Diseases, Mass transfer, Numerical methods, Perturbation techniques, Asymptotic method, Concentrated influence, Condition, Dynamic system with delay, Infectious disease, Infectious disease models, Singularly perturbed problem, Sorption therapy, Systems with delays, Viral infections, Adsorption

Cite:
Baranovsky S.V., Bomba A.Y. (2023). Generalizing the infectious disease model taking into account diffusion perturbations, logistics dynamics, and biostimulation. Cybernetics and Systems Analysis, 59 (1), 156–168. doi: https://doi.org/10.1007/s10559-023-00595-x http://jnas.nbuv.gov.ua/article/UJRN-0001380512 [In Ukrainian].