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A novel method for basic reproduction ratio of a diffusive size-structured population model with delay

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Abstract

In this paper, we discuss a new size-structured population model with a delay in birth process. The focus is to discuss the existence and the uniqueness results along with basic reproduction ratio \((R_{0})\). The birth function h is not necessarily a Ricker type of function but expression of \(R_{0}\) obtained in this paper works for a more general function h. This analysis covers a larger class of models. The model is converted into an abstract form and then theory of semigroup is used to obtain the results. The basic reproduction number is constructed as spectral radius of the next generation operator. The form for basic reproduction ratio is very general and can be applied to other models as well. We also solve the model numerically to study the effect of delay on population distribution.

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Data availability statement

No datasets are associated with this manuscript. The datasets used for generating the plots and results during the current study can be directly obtained from the numerical simulation of the related mathematical equations in the manuscript.

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Acknowledgements

We are thankful to the anonymous reviewers for their valuable comments and suggestions, which helps us to improve our manuscript.

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Authors and Affiliations

  1. School of Basic Sciences, Indian Institute of Technology Mandi, 175005, Kamand, H.P., India

    Manoj Kumar & Syed Abbas

  2. Department of Mathematical Sciences, United Arab Emirates University, P.O. Box 15551, Al Ain, UAE

    Abdessamad Tridane

Authors
  1. Manoj Kumar
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  2. Syed Abbas
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  3. Abdessamad Tridane
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Correspondence to Abdessamad Tridane.

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Kumar, M., Abbas, S. & Tridane, A. A novel method for basic reproduction ratio of a diffusive size-structured population model with delay. Nonlinear Dyn 109, 3189–3198 (2022). https://doi.org/10.1007/s11071-022-07558-5

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  • DOI: https://doi.org/10.1007/s11071-022-07558-5

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