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Dynamical analysis for an age-structured model of eating disorders

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Abstract

This paper investigates the diffusion of eating disorders by constructing an age-structured model with an age-dependent diffusion coefficient. Compared with earlier articles, we introduce the process of re-susceptibility and consider the role of education, which is equivalent to vaccination, without permanent immunity to eating disorders. We also demonstrate the existence of a unique positive solution for this non-local model by using the semigroup theory. Furthermore, the local and global stability of the disease-free equilibrium state is examined when the effective reproduction number satisfies certain conditions, which is theoretically important and meaningful in controlling the development of eating disorders. Several numerical simulations support our theoretical analysis and reveal how education and medical resources affect the distribution of eating disorders.

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Acknowledgements

The authors are grateful to the editors and the anonymous reviewers for their careful reading, valuable comments and constructive suggestions, which have helped us to improve the quality of the paper.

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  1. School of Information Engineering, Zhejiang Ocean University, Zhoushan, 316022, China

    Wenhao Dai & Hailiang Zhang

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  1. Wenhao Dai
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  2. Hailiang Zhang
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Correspondence to Hailiang Zhang.

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Dai, W., Zhang, H. Dynamical analysis for an age-structured model of eating disorders. J. Appl. Math. Comput. 69, 1887–1901 (2023). https://doi.org/10.1007/s12190-022-01814-y

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