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On a Chemotactic Host–Pathogen Model: Boundedness, Aggregation, and Segregation

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Abstract

This study formulates a host–pathogen model driven by cross-diffusion to examine the effect of chemotaxis on solution dynamics and spatial structures. The negative binomial incidence mechanism is incorporated to illustrate the transmission process by pathogens. In terms of the magnitude of chemotaxis, the global solvability of the model is extensively studied by employing semigroup methods, loop arguments, and energy estimates. In a limiting case, the necessary conditions for chemotaxis-driven instability are established regarding the degree of chemotactic attraction. Spatial aggregation may occur along strong chemotaxis in a two-dimensional domain due to solution explosion. We further observe that spatial segregation appears for short-lived free pathogens in a one-dimensional domain, whereas strong chemotactic repulsion homogenizes the infected hosts and thus fails to segregate host groups effectively.

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Data sharing was not applicable to this article as no datasets were generated or analyzed during the current study.

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Acknowledgements

We would like to thank Yurij Salmaniw for his discussion and assistance in support of this work. The research of the second author was partially supported by the Natural Sciences and Engineering Research Council of Canada (Individual Discovery Grant RGPIN-2020-03911 and Discovery Accelerator Supplement Award PGPAS-2020-00090) and the Canada Research Chairs program (Tier 1 Canada Research Chair Award). The research of the third author was partially supported by the National Natural Science Foundation of China (No. 11571200) and the Natural Science Foundation of Shandong Province (No. ZR2021MA062).

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Authors and Affiliations

  1. School of Mathematics, Shandong University, Jinan, 250100, China

    Guodong Liu & Xiaoyan Zhang

  2. Interdisciplinary Lab for Mathematical Ecology and Epidemiology, Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, T6G 2G1, Canada

    Guodong Liu & Hao Wang

Authors
  1. Guodong Liu
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  2. Hao Wang
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  3. Xiaoyan Zhang
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Contributions

G.L. and H.W. proposed the idea and methodology. G.L. performed analysis and simulations. G.L. and H.W. wrote the main manuscript text. All authors reviewed and revised the manuscript.

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Correspondence to Hao Wang.

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Communicated by Kevin Painter.

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Liu, G., Wang, H. & Zhang, X. On a Chemotactic Host–Pathogen Model: Boundedness, Aggregation, and Segregation. J Nonlinear Sci 34, 32 (2024). https://doi.org/10.1007/s00332-023-10010-6

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