Global dynamics of a delayed epidemic model with latency and relapse

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Abstract
A mathematical model describing the transmission dynamics of an infectious disease with an exposed (latent) period, relapse and a saturation incidence rate is investigated. By analyzing the corresponding characteristic equations, the local stability of a disease-free equilibrium and an endemic equilibrium is established. By using suitable Lyapunov functionals and LaSalle’s invariance principle, it is proven that if the basic reproduction number is less than unity, the diseasefree equilibrium is globally asymptotically stable and therefore the disease fades out; and if the basic reproduction number is greater than unity, the endemic equilibrium is globally asymptotically stable and the disease becomes endemic.

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