Analysis of a Fractional-order “SVEIR” Epidemic Mo del with a General Nonlinear Saturated Incidence Rate in a Continuous Reactor
Miled El Hajji *
ENIT-LAMSIN, BP. 37, 1002 Tunis-Belv´ed`ere, Tunis El Manar University, Tunisia
Sayed Sayari
ENIT-LAMSIN, BP. 37, 1002 Tunis-Belv´ed`ere, Tunis El Manar University, Tunisia and Higher Institute of Environmental Technologies of Urban Planning and Building, 2 Rue de l’Artisanat Charguia 2, 2035 Tunis, Carthage university, Tunisia.
*Author to whom correspondence should be addressed.
Abstract
In this paper, I propose a fractional-order mathematical five-dimensional dynamical system modeling a SVEIR model of infectious disease transmission in a chemostat. A profound qualitative analysis is given. The analysis of the local and global stability of equilibrium points is carried out. It is proved that if R > 1, then the disease-persistence (endemic) equilibrium is globally asymptotically stable. However, if R ≤ 1, then the disease-free equilibrium is globally asymptotically stable in R 5. Finally, some numerical tests are done using the ”PECE” method in order to validate the obtained results.
Keywords: Fractional-Order SVEIR model, caputo fractional derivative, equilibrium points, local and global stability, direct Lyapunov Method, LaSalle’s invariance principle.