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Dynamics of a single-strain and two-strain respiratory infection driven by travel on a metapopulation network

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Abstract

We formulate a compartmental model for the propagation of a respiratory disease in a patchy environment. The patches are connected through the mobility of individuals, and we assume that disease transmission as well as recovery are possible during travel. Moreover, the migration terms are assumed to depend on the distance between patches and the perceived severity of the disease. The positivity and boundedness of the model solutions are discussed. We analytically show the existence and global asymptotic stability of the disease-free equilibrium. We study three different network topologies numerically and find that underlying network structure is crucial for disease transmission. Further numerical simulations reveal that infection during travel has the potential to change the stability of disease-free equilibrium from stable to unstable. The coupling strength and transmission coefficients are also very crucial in disease propagation. Different exit screening scenarios indicate that the origin patch may have adverse effects but other patches will be benefited from exit screening. Furthermore, we modify the model to incorporate emergence of a second strain. Numerical simulations indicate that two co-circulating strains will not persist simultaneously in the community but only one of the strains may persist in the long run. Transmission coefficients corresponding to the second strain are very crucial and show threshold like behavior with respect to the equilibrium density of the second strain.

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Data Availability

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

Notes

  1. https://github.com/indrajitg-r/Metapop_IDT.

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Acknowledgements

We would like to thank the expert reviewers and the learned handling editor for their valuable comments and suggestions, which helped us improve the quality of the manuscript.

Funding

Research of IG is supported by National Board for Higher Mathematics (NBHM) postdoctoral fellowship (Ref. No: 0204/3/2020/R & D-II/2458). SSN receives a Senior Research Fellowship from CSIR, Government of India, New Delhi. The work of SR is partially supported by SERB MATRICS grants MTR/2020/000186 and MSC/2020/00028 of the Government of India.

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Authors and Affiliations

  1. Department of Computational and Data Sciences, Indian Institute of Science, Bengaluru, Karnataka, 560012, India

    Indrajit Ghosh, Soumyendu Raha & Debnath Pal

  2. Center for Health Emergencies, Bruno Kessler Foundation, 38122, Trento TN, Italy

    Sk Shahid Nadim

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  1. Indrajit Ghosh
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  2. Sk Shahid Nadim
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Correspondence to Indrajit Ghosh.

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Ghosh, I., Nadim, S.S., Raha, S. et al. Dynamics of a single-strain and two-strain respiratory infection driven by travel on a metapopulation network. Nonlinear Dyn 111, 21371–21389 (2023). https://doi.org/10.1007/s11071-023-08952-3

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