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

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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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Authors and Affiliations

  1. School of Science, Xi’an Polytechnic University, Xi’an, 710048, People’s Republic of China

    Qiaoling Chen

  2. School of Mathematics and Information Science, Shaanxi Normal University, Xi’an, 710062, People’s Republic of China

    Qiaoling Chen

  3. School of Mathematical Sciences, Dalian University of Technology, Dalian, 116024, People’s Republic of China

    Fengquan Li

  4. College of Mathematics and System Sciences, Xinjiang University, Urumqi, 830046, People’s Republic of China

    Zhidong Teng

  5. School of Mathematics and Statistics, Xidian University, Xi’an, 710071, People’s Republic of China

    Feng Wang

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  1. Qiaoling Chen
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  4. Feng Wang
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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 34, 1209–1236 (2022). https://doi.org/10.1007/s10884-020-09934-4

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