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

• Published in: Journal of the Franklin Institute 2020-05, Vol.357 (7), p.4414-4436
• Main Authors: Lahrouz, Aadil, Settati, Adel, Mahjour, Hamza El, Jarroudi, Mustapha El, Fatini, Mohamed El
• Format: Article
• Language: English
• Subjects: Asymptotic properties; Complex network; Computer simulation; Demographics; Epidemics; Liapunov functions; Mathematical functions; Mathematical models; SIRI model; Stability; Topology
• ISSN: 0016-0032; 1879-2693; 0016-0032
• DOI: 10.1016/j.jfranklin.2020.03.010

•A new epidemic model on complex networks is proposed.•Necessary and sufficient conditions for the stability of equilibriums is established.•The influence of heterogeneous network structure on the epidemic outcome is discussed. 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 R0 which strictly depends on the topology of the underlying network and the model parameters. Second, we show that R0 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 R0≤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.