Modeling small-scale spatially distributed influences on the development of infectious diseases

: pp. 310–321
Received: May 06, 2020
Revised: July 22, 2020
Accepted: July 24, 2020
National University of Water and Environmental Engineering
Rivne State Humanitarian University
Victor Polishchuk Regional Clinical Medical and Diagnostic Center by Rivne
National University of Water and Environmental Engineering

In this paper, the small-scale spatially distributed influences on the infectious disease development are proposed to be modeled by means of diffuse disturbance of the corresponding degenerate model problems.  We represent the asymptotic expansions of the solutions of the corresponding singularly-disturbed problems with a time-delay that are reduced to a sequence of problems without a time-delay.  The results of numerical experiments that characterize the spatially distributed diffuse influences on the infectious disease development are presented.  The decrease in the maximum concentration level of pathogenic antigens due to their diffuse ``redistribution'' from the locus of infection into less infected areas of the target organ is illustrated.

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Mathematical Modeling and Computing, Vol. 7, No. 2, pp. 310–321 (2020)