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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 |

### Keywords:

delay differential equations; steady states; periodic solutions; stability analysis; relaxation method; Newton type method; Fourier series expansion
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\textit{M. Yu. Khristichenko} and \textit{Yu. M. Nechepurenko}, Russ. J. Numer. Anal. Math. Model. 36, No. 2, 87--99 (2021; Zbl 1466.92192)

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### References:

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