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Modelling the dynamics of online food delivery services on the spread of food-borne diseases

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Abstract

We propose and analyze a deterministic mathematical model for the transmission of food-borne diseases in a population consisting of humans and flies. We employ the Caputo operator to examine the impact of governmental actions and online food delivery services on the transmission of food-borne diseases. The proposed model investigates important aspects such as positivity, boundedness, disease-free equilibrium, basic reproduction number and sensitivity analysis. The existence and uniqueness of a solution for the initial value problem is established using Banach and Schauder type fixed point theorems. Functional techniques are employed to demonstrate the stability of the proposed model under the Hyers–Ulam condition. For an approximate solution, the iterative fractional order Predictor–Corrector scheme is utilized. The simulation of this scheme is conducted using Matlab as the numeric computing environment, with various fractional order values ranging from 0.75 to 1. Over time, all compartments demonstrate convergence and stability. The numerical simulations highlight the necessity for the government to implement the most effective food safety control interventions. These measures could involve food safety awareness and training campaigns targeting restaurant managers, staff members involved in online food delivery, as well as food delivery personnel.

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The authors confirms that the data supporting the findings of this study are available within the article.

Code availability

Matlab code is available from the author on reasonable request.

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Acknowledgements

This work was partially supported by the Fundação para a Ciência e a Tecnologia, I.P. (FCT, Funder ID = 50110000187) under Grants UIDB/04106/2020 and UIDP/04106/2020 (CIDMA); and Project 2022.03091.PTDC (CoSysM3).

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Authors and Affiliations

  1. College of Computer and Information Science, University of Arkansas at Little Rock, Little Rock, AR, 72204, USA

    Emmanuel Addai & Mary Nwaife Mezue

  2. Department of Mathematics, Center for Research and Development in Mathematics and Applications (CIDMA), University of Aveiro, 3810-193, Aveiro, Portugal

    Delfim F. M. Torres

  3. Faculty of Sciences and Technology (FCT), Research Center in Exact Sciences (CICE), University of Cape Verde (Uni-CV), 7943-010, Praia, Cape Verde

    Delfim F. M. Torres

  4. Department of Logistics and Sustainable Transport, University of Maryland, College Park, MD, 20740, USA

    Zalia Abdul-Hamid

  5. Department of Mathematics, Saveetha School of Engineering SIMATS, Chennai, India

    Joshua Kiddy K. Asamoah

  6. Department of Mathematics, Kwame Nkrumah University of Science and Technology, Kumasi, Ghana

    Joshua Kiddy K. Asamoah

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  1. Emmanuel Addai
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  2. Delfim F. M. Torres
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  3. Zalia Abdul-Hamid
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  4. Mary Nwaife Mezue
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  5. Joshua Kiddy K. Asamoah
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The authors confirms sole responsibility for study conceptualization, methodology, formal analysis, codes writing, manuscript writing and editing, and approval of the final manuscript draft.

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Correspondence to Joshua Kiddy K. Asamoah.

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Addai, E., Torres, D.F.M., Abdul-Hamid, Z. et al. Modelling the dynamics of online food delivery services on the spread of food-borne diseases. Model. Earth Syst. Environ. (2024). https://doi.org/10.1007/s40808-024-02046-8

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