Analysis of a Fractional-order “SVEIR” Epidemic Mo del with a General Nonlinear Saturated Incidence Rate in a Continuous Reactor

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.

Mathematical study for the phase-based transmissibility of a novel COVID-19 Coronavirus

“…Further, by Lemma 1, Ω 2 is a compact, absorbing subset of R 5 + , and the largest compact invariant set in {(S, E, I, R,W ) ∈ Ω 2 :V 1 = 0} is {Q}. Therefore, by the Lasalle's invariance principle (see, for instance, [15,Theorem 3.1] and [7,8,9,10,11,12,13,14] for other applications), every solution of system (1) with initial conditions in R 5 + converges toQ as t → +∞.…”

“…This epidemic obliges us to propose models allowing to estimate the transmissibility and dynamic of the transmission of the virus. There were several researches focusing on mathematical modelling [6,7,8]. However, the transmission route form the seafood market to people were not considered in the published models.…”

Mathematical Analysis of a Fractional-order "SIR" Epidemic Model with a General Nonlinear Saturated Incidence Rate in a Chemostat

“…+ , the closed non-negative cone in R 3 , is positively invariant [22,23,24,25,4,26,27,28,29,30,31,32,33] for the system (2.6). More precisely, Proposition 1.…”

How the Fractional-order Improve and Extend the Well-known Competitive Exclusion Principle in the Chemostat Model with n Species Competing for a Single Resource?

“…+ , the closed non-negative cone in R n+1 , is positively invariant [22,23,24,25,26,15,17,16,27,28,12,29,18,13]…”