Title: A discrete viral infection model with both modes of transmission and distributed delays

Authors: Brahim El Boukari; Khalid Hattaf; Jalila El Ghordaf

Addresses: Higher School of Technology, Sultan Moulay Slimane University, 23000 Beni Mellal, Morocco ' Centre Régional des Métiers de l'Education et de la Formation (CRMEF), 20340 Derb Ghalef, Casablanca, Morocco ' Faculty of Sciences and Techniques, Applied Mathematics and Scientific Computing Laboratory (LMACS), Sultan Moulay Slimane University, 23000 Beni Mellal, Morocco

Abstract: The aim of this work is to propose and analyse a discrete virus dynamics model with distributed delays and both modes of transmission, one by virus-to-cell infection and the other by cell-to-cell transfer. In the proposed model, the first distributed delays describes the time needed for infected cells to produce new virions, and the second portrays the time necessary for the newly produced virions to become mature and infectious. In addition, the infection transmission process is modelled by general incidence functions for both modes. Furthermore, we prove that the proposed discrete model has the same dynamics as the corresponding continuous model, such as positivity, boundedness and global behaviours of solutions with no restriction on the time step size. Moreover, numerical simulations are given to illustrate and confirm our main analytical results.

Keywords: viral infection; distributed delay; difference equation; global stability.

DOI: 10.1504/IJDSDE.2021.113903

International Journal of Dynamical Systems and Differential Equations, 2021 Vol.11 No.1, pp.31 - 44

Received: 29 Mar 2019
Accepted: 07 May 2019
Published online: 01 Apr 2021 *

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