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This work is devoted to the mathematical analysis of a COVID‐19 two‐strain epidemic model. The COVID‐19 mathematical model described the infection forces of each strain by a nonmonotonic incidence function. First, we establish the well‐posedness of the COVID‐19 stochastic model in terms of existence and uniqueness of the global positive solution. After that, we investigate the results of the stochastic extinction and persistence in mean of the COVID‐19 disease. The findings show that both strains of COVID‐19 pandemic extinct, when the basic reproduction number is less than unity. If the latter is not achieved, then the infection related to the strain with higher stochastic basic reproduction number will persist. Additionally, both strains can persist at the same time, if their related stochastic basic reproduction numbers are both greater than one. Finally, various numerical simulations are carried out in order to validate the theoretical findings concerning the extinction and persistence in mean of the disease. As an application of our work, we have chosen to compare our deterministic and stochastic results with COVID‐19 clinical data. [ABSTRACT FROM AUTHOR]

In this paper, we study mathematically a two strains epidemic model taking into account non-monotonic incidence rates and vaccination strategy. The model contains seven ordinary differential equations that illustrate the interaction between the susceptible, the vaccinated, the exposed, the infected and the removed individuals. The model has four equilibrium points, namely, disease free equilibrium, endemic equilibrium with respect to the first strain, endemic equilibrium with respect to the second strain and the endemic equilibrium with respect to both strains. The global stability of the equilibria has been demonstrated using some suitable Lyapunov functions. The basic reproduction number is found depending on the first strain reproduction number R 0 1 and the second reproduction number R 0 2. We have shown that the disease dies out when the basic reproduction number is less than unity. It was remarked that the global stability of the endemic equilibria depends, on the strain basic reproduction number and on the strain inhibitory effect reproduction number. We have also observed that the strain with high basic reproduction number will dominate the other strain. Finally, the numerical simulations are presented in the last part of this work to support our theoretical results. We notice that our suggested model has some limitations and does not predicting the long-term dynamics for some reproduction numbers cases. [ABSTRACT FROM AUTHOR]

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-1 and 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 the steady states. However, the time of convergence toward these states depends on the value of the fractional order derivative. [ABSTRACT FROM AUTHOR]