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Computation of periodic solutions to models of infectious disease dynamics and immune response. (English) Zbl 1466.92192

Summary: The paper is focused on computation of stable periodic solutions to systems of delay differential equations modelling the dynamics of infectious diseases and immune response. The method proposed here is described by an example of the well-known model of dynamics of experimental infection caused by lymphocytic choriomeningitis viruses. It includes the relaxation method for forming an approximate periodic solution, a method for estimating the approximate period of this solution based on the Fourier series expansion, and a Newton-type method for refining the approximate period and periodic solution. The results of numerical experiments are presented and discussed. The proposed method is compared to known ones.

MSC:

92D30 Epidemiology
34K13 Periodic solutions to functional-differential equations
34L16 Numerical approximation of eigenvalues and of other parts of the spectrum of ordinary differential operators
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