Mathematical analysis of a fractional order two strain SEIR epidemic model
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two-strain SEIR, epidemic modelAbstract
In this paper, a fractional order two-strain SEIR epidemic model is studied and analyzed. This model will be presented in the form of a system containing six fractional order equations, that illustrate the interactions between susceptible, strain-1 exposed, strain-2 exposed, strain-1 infected, strain-2 infected and removed individuals. The proposed model has four equilibrium points: the disease-free equilibrium point, the strain-1 equilibrium point, the strain-2 equilibrium point and the total equilibrium point. By determining the new generation matrix, we have shown that our model has two basic reproduction numbers R1 0 and R2 0; the first one is associated with the strain-1and the second one is related to the strain-2. Using the Lyapunov method and La-Salle’s invariance principle, we have proved the global stability of the different equilibrium points, this stability depends on the strain-1 reproduction number R1 0 and on the strain-2 reproduction number R2 0. Finally, numerical simulations are presented to value our theoretical results. More precisely, if the two basic reproduction numbers are less than or equal 1, then the disease-free equilibrium point is globally asymptotically stable, if one of the basic reproduction numbers is less than or equal 1 and the other is greater than 1, then the equilibrium point associated with the greatest basic reproduction number is globally asymptotically stable, and if the two basic reproduction numbers are greater than 1, then the last equilibrium point is globally asymptotically stable. Moreover, we have shown that the change in the fractional order value has no effect on the stability of thesteady states. However, the time of convergence toward these states depends on the value of the fractional order derivative.
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