Global Dynamics and Asymptotic Spreading Speeds for a Partially Degenerate Epidemic Model with Time Delay and Free Boundaries

Abstract

This paper concerns the global dynamics and asymptotic spreading speeds for a partially degenerate epidemic model with time delay and free boundaries. Given a suitable compatible condition for initial values, we establish the global well-posedness of solutions and provide some sufficient conditions for spreading and vanishing. When spreading occurs, we prove that the asymptotic spreading speed is uniquely determined by a semi-wave problem with time delay. To investigate the existence of monotone increasing solutions to the semi-wave problem, we give a distribution of solutions to a third degree exponential polynomial equation. The results show that time delay slows down the asymptotic spreading speed of the disease.

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Acknowledgements

We are very grateful to the anonymous referee for a careful reading and valuable suggestions that improve our paper. Chen’s work was supported by NSFC (No: 11801432), China Postdoctoral Science Foundation (No: 2019M663610) and the Young Talent fund of University Association for Science and Technology in Shaanxi (No: 20200510). Li’s work was supported by NSFC (No: 11571057). Teng’s work was supported by NSFC (No: 11771373). Wang’s work was supported by NSFC (No: 11801429) and the Natural Science Basic Research Plan in Shaanxi Province of China (No: 2019JQ-136).

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Correspondence to Qiaoling Chen.

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Chen, Q., Li, F., Teng, Z. et al. Global Dynamics and Asymptotic Spreading Speeds for a Partially Degenerate Epidemic Model with Time Delay and Free Boundaries. J Dyn Diff Equat (2021). https://doi.org/10.1007/s10884-020-09934-4

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Keywords

  • Free boundary
  • Time delay
  • Semi-waves
  • Spreading speed
  • Spreading and vanishing