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In this paper, we consider an SEIS epidemic model with infectious force in latent and infected period, which incorporates by nonlinear incidence rates. The local stability of the equilibria is discussed. By means of Lyapunov functionals and LaSalle's invariance principle, we proved the global asymptotic stability of the disease-free equilibrium and the endemic equilibrium. An application is given and numerical simulation results based on real data of COVID-19 in Morocco are performed to justify theoretical findings.

Threshold Dynamics of an $$\mathbf {SEIS}$$ Epidemic Model with Nonlinear Incidence Rates