Oscillatory Behaviors of an Epidemiological Model on Small-World Networks

Abstract

We investigate the oscillatory dynamics of an epidemiological model of SIRS(susceptible-infectiverecovered-susceptible) type on small-world networks. A delay differential equation for the infected population is derived to show that three characteristic patterns, stationarity, oscillation, and synchronized extermination exist, depending on the competition between the disease's life cycle and the time for it to sweep the world. Numerical calculations support this prediction and suggest that the synchronization parameter proposed by Kuramoto can be a good measure of patterns.

Synchronization and extinction in a high-infectivity spatial SIRS with long-range links

“…The above scaling relations have been observed in e.g. stochastic Lotka-Volterra models [24][25][26], stochastic SIRS models [11,12], SIR model with removal-renewal [10], and generalized Lotka-Volterra models [27].…”

“…So it would appear that SIRS does not synchronize in finite dimensions, although it does [8] on SW networks, which are eectively ∞-dimensional [35]. Notice that Ki Baek [12] has discussed approximate arguments suggesting why this might actually be the case.…”

“…(2019) 013203 be propagated in time. A dierent type of extinction thus occurs when a synchronized orbit passes too close to the absorbing state and the dynamics gets attracted to it [8,12]. This last case of synchronization-mediated extinctions is the focus of the present work.…”

“…When α → 0, on the other hand, long links are generated and an ∞-dimensional [35,49] random graph is produced. In this article, the eects of spatial dimension d and the distribution of link lengths parametrized by α are analyzed for a SIRS [8,11,12,50,51] model of excitable dynamics on these networks. The focus of the present work is on the analysis of synchronization and the characterization of synchronization-mediated extinction times in these networks.…”

Proximity effect in La0.7Sr0.3MnO3/Bi2Sr2CaCu2O8hybrid bi-layers

“…The M-H loop of the B5 single layer measured at 5 K (figure 8(a)) displays the superconducting diamagnetic property of Bi-2212 with a characteristic star-like curve with a finite pinning force. Whereas, the L4/B5 bi-layer, having the thinnest (40 nm) LSMO underlayer, shows a deformed superconducting loop with a observable ferromagneticlike feature (figure 8(b)), which results from the partial suppression of the superconducting order parameter due to the presence of the ferromagnetic LSMO underlayer [33,34].…”