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Effect of family and public health education in drug transmission: an epidemiological model with memory

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Abstract

A problem of theoretical and numerical interest in standard epidemiological models is the calculation or estimation of the basic reproduction number \({\mathcal {R}}_0\). This parameter serves as a threshold quantity for the extinction or spread of the disease. In this paper, we explore a model of drug transmission based on compartmental dynamic models, as in epidemiological models of infectious diseases. The objective is to study \({\mathcal {R}}_0\) as a function of family and public health education. In order to make the general analysis and obtain a wide range of results, we use a fractional time-Caputo derivative instead of the classical time derivative. The analytic and numerical results (existence and uniqueness of solutions, equilibrium stability analysis, parameter sensitivity, trapezoidal rule, and fractional Euler method) showed that the combination of family education and public health has an impact on drug transmission reduction. This can be used to control or adopt treatment strategies.

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Author notes

  1. A. Alla Hamou, E. Azroul, G. Diki and M. Guedda have contributed equally to this work.

Authors and Affiliations

  1. Faculty of Sciences, Mohammed V University in Rabat, B.P. 1014, Rabat, Morocco

    A. Alla Hamou

  2. Laboratory of Mathematical Analysis and Applications, Faculty of Sciences Dhar Al Mahraz, Sidi Mohamed Ben Abdellah University, 30000, Fez, Morocco

    E. Azroul & G. Diki

  3. LAMFA, CNRS UMR, Department of Mathematics, Picardie Jules Verne University, Amiens, 7352, France

    M. Guedda

Authors
  1. A. Alla Hamou
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  2. E. Azroul
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  3. G. Diki
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  4. M. Guedda
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Correspondence to G. Diki.

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Alla Hamou, A., Azroul, E., Diki, G. et al. Effect of family and public health education in drug transmission: an epidemiological model with memory. Model. Earth Syst. Environ. 9, 2809–2828 (2023). https://doi.org/10.1007/s40808-022-01662-6

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  • DOI: https://doi.org/10.1007/s40808-022-01662-6

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