Computation of periodic solutions to models of infectious disease dynamics and immune response
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M. Yu. Khristichenko
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Yu. M. Nechepurenko
Abstract
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.
Funding statement: The research was supported by the Moscow Center for Fundamental and Applied Mathematics (agreement with the Ministry of Education and Science of the Russian Federation No. 075–15–2019–1624) (numerical experiments and analysis of their results) and the Russian Science Foundation (Grant No. 17–71–20149) (development and implementation of proposed numerical methods).
Acknowledgment
The authors are grateful to the reviewers for their useful comments.
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© 2021 Walter de Gruyter GmbH, Berlin/Boston
Artikel in diesem Heft
- Frontmatter
- Runge–Kutta discontinuous Galerkin method for Baer–Nunziato model with ‘simple WENO’ limiting of conservative variables
- Influence of unbroken clouds stochastic structure on the solar radiation transfer with results of Monte Carlo simulation
- Computation of periodic solutions to models of infectious disease dynamics and immune response
- Modelling of hydrogen-air supersonic mixing and combustion in near-wall region
- Analysis of the predictability of stratospheric variability and climate indices based on seasonal retrospective forecasts of the INM RAS climate model
Artikel in diesem Heft
- Frontmatter
- Runge–Kutta discontinuous Galerkin method for Baer–Nunziato model with ‘simple WENO’ limiting of conservative variables
- Influence of unbroken clouds stochastic structure on the solar radiation transfer with results of Monte Carlo simulation
- Computation of periodic solutions to models of infectious disease dynamics and immune response
- Modelling of hydrogen-air supersonic mixing and combustion in near-wall region
- Analysis of the predictability of stratospheric variability and climate indices based on seasonal retrospective forecasts of the INM RAS climate model
