UDC 519.6
1 Educational and Scientific Institute of Automatics, Cybernetics, and Computer Engineering of the National University of Water and Environmental Engineering, Rivne, Ukraine
 svbaranovsky@gmail.com
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2 Educational and Scientific Institute of Automatics, Cybernetics, and Computer Engineering of the National University of Water and Environmental Engineering, Rivne, Ukraine
abomba@ukr.net
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GENERALIZING THE INFECTIOUS DISEASE MODEL TAKING INTO ACCOUNT
DIFFUSION PERTURBATIONS, LOGISTICS DYNAMICS, AND BIOSTIMULATION
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 of 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,” only biostimulation 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.
Keywords: infectious disease model, biostimulation, dynamic systems with delay, asymptotic methods, singularly perturbed problems, concentrated influences, logistics dynamics.
full text
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