Global dynamics of an epidemic model with incomplete recovery in a complex network

Abstract In this work, we study the global dynamics of a new SIRI epidemic model with demographics, graded cure and relapse in a complex heterogeneous network. First, we analytically make out the epidemic threshold R 0 which strictly depends on the topology of the underlying network and the model parameters. Second, we show that R 0 plays the role of a necessary and sufficient condition between extinction and permanence of the disease. More specifically, by using new Lyapunov functions, we establish that the disease free-equilibrium state E0 is globally asymptotically stable when R 0 ≤ 1 , otherwise we proved the existence and uniqueness of the endemic state E*. Then, we show that E* is globally asymptotically stable. Finally, we present a series of numerical simulations to confirm the correctness of the established analytical results.

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