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Periodic and almost periodic solutions for a non-autonomous respiratory disease model with a lag effect

Abstract

This paper studies a kind of non-autonomous respiratory disease model with a lag effect. First of all, the permanence and extinction of the system are discussed by using the comparison principle and some differential inequality techniques. Second, it assumes that all coefficients of the system are periodic. The existence of positive periodic solutions of the system is proven, based on the continuation theorem in coincidence with the degree theory of Mawhin and Gaines. In the meantime, the global attractivity of positive periodic solutions of the system is obtained by constructing an appropriate Lyapunov functional and using the Razumikin theorem. In addition, the existence and uniform asymptotic stability of almost periodic solutions of the system are analyzed by assuming that all parameters in the model are almost periodic in time. Finally, the theoretical derivation is verified by a numerical simulation.

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Corresponding author

Correspondence to Longxing Qi.

Additional information

This research was supported by the National Natural Science Foundation of China (11401002, 11771001), the Natural Science Foundation of Anhui Province (2008085MA02), the Natural Science Fund for Colleges and Universities in Anhui Province (KJ2018A0029), the Teaching Research Project of Anhui University (ZLTS2016065), the Quality engineering project of colleges and universities in Anhui Province (2020jyxm0103), and the Science Foundation of Anhui Province Universities (KJ2019A005).

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Shi, L., Qi, L. & Zhai, S. Periodic and almost periodic solutions for a non-autonomous respiratory disease model with a lag effect. Acta Math Sci 42, 187–211 (2022). https://doi.org/10.1007/s10473-022-0110-3

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  • DOI: https://doi.org/10.1007/s10473-022-0110-3

Key words

  • respiratory disease
  • lag effect
  • periodic solution
  • almost periodic solution
  • Lyapunov functional

2010 MR Subject Classification

  • 34A40
  • 34C10
  • 34D23
  • 92B05