This paper investigates the global stability analysis of two-strain epidemic model with two general incidence rates. The problem is modelled by a system of six nonlinear ordinary differential equations describing the evolution of susceptible, exposed, infected and removed individuals. The wellposedness of the suggested model is established in terms of existence, positivity and boundedness of solutions. Four equilibrium points are given, namely the disease-free equilibrium, the endemic equilibrium with respect to strain 1, the endemic equilibrium with respect to strain 2, and the last endemic equilibrium with respect to both strains. By constructing suitable Lyapunov functional, the global stability of the disease-free equilibrium is proved depending on the basic reproduction number \(R_0\). Furthermore, using other appropriate Lyapunov functionals, the global stability results of the endemic equilibria are established depending on the strain 1 reproduction number \(R^{1}_0\) and the strain 2 reproduction number \(R^{2}_0\). Numerical simulations are performed in order to confirm the different theoretical results. It was observed that the model with a generalized incidence functions encompasses a large number of models with classical incidence functions and it gives a significant wide view about the equilibria stability. Numerical comparison between the model results and COVID-19 clinical data was conducted. Good fit of the model to the real clinical data was remarked. The impact of the quarantine strategy on controlling the infection spread is discussed. The generalization of the problem to a more complex compartmental model is illustrated at the end of this paper.

本文研究了具有两种一般发病率的两株流行病模型的全局稳定性分析。该问题由一个由六个非线性常微分方程组成的系统建模，该方程描述了易感个体、暴露个体、感染个体和被移除个体的演变。所建议模型的适定性是根据解的存在性、正性和有界性来建立的。给出了四个平衡点，即无病平衡点、菌株 1 的地方病平衡点、菌株 2 的地方病平衡点和两个菌株的最后一个地方病平衡点。通过构造合适的 Lyapunov 泛函，证明了无病平衡的全局稳定性取决于基本再生数\(R_0\). 此外，使用其他适当的 Lyapunov 泛函，地方性平衡的全局稳定性结果取决于菌株 1 的再生数\(R^{1}_0\)和菌株 2 的再生数\(R^{2}_0\ ). 进行数值模拟以确认不同的理论结果。据观察，具有广义关联函数的模型包含大量具有经典关联函数的模型，并且它对平衡稳定性提供了显着的宽广视野。对模型结果和 COVID-19 临床数据进行了数值比较。模型与真实临床数据的良好拟合得到了评价。讨论了隔离策略对控制感染传播的影响。本文最后说明了将问题推广到更复杂的隔间模型。