Global dynamics of an epidemic model with incomplete recovery in a complex network (2020)

Authors: A Lahrouz, A Settati, H El Mahjour, M El Jarroudi et al. ↩

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 $E^{0}$ is globally asymptotically stable when $R_{0} \leq 1$, 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.

Reference

Franklin Institute 357.7, pp. 4414-4436. DOI: 10.1016/j.jfranklin.2020.03.010 ↩