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

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.

infectious disease model
stationary solutions for dynamic systems
stability of solution
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