Transition from time-variant to static networks: Timescale separation in N-intertwined mean-field approximation of susceptible-infectious-susceptible epidemics.

We extend the N-intertwined mean-field approximation (NIMFA) for the susceptible-infectious-susceptible (SIS) epidemiological process to time-varying networks. Processes on time-varying networks are often analyzed under the assumption that the process and network evolution happen on different timescales. This approximation is called timescale separation. We investigate timescale separation between disease spreading and topology updates of the network. We introduce the transition times [under T]̲(r) and T[over ¯](r) as the boundaries between the intermediate regime and the annealed (fast changing network) and quenched (static network) regimes, respectively, for a fixed accuracy tolerance r. By analyzing the convergence of static NIMFA processes, we analytically derive upper and lower bounds for T[over ¯](r). Our results provide insights and bounds on the time of convergence to the steady state of the static NIMFA SIS process. We show that, under our assumptions, the upper-transition time T[over ¯](r) is almost entirely determined by the basic reproduction number R_{0} of the network. The value of the upper-transition time T[over ¯](r) around the epidemic threshold is large, which agrees with the current understanding that some real-world epidemics cannot be approximated with the aforementioned timescale separation.

First Clinical Experience With Ophthalmic e-Device for Unaided Patient Self-Examination During COVID-19 Lockdown.

PURPOSE: The aim of this study was to describe a new type of medical device that allows for internet-enabled patient self-screening, without the aid of an ophthalmic professional, through biomicroscopy self-imaging and self-measurement of the best-corrected visual acuity (BCVA). METHODS: In this prospective nonrandomized comparative study, 56 patients were instructed to screen their own eyes using a custom-built e-Device containing miniaturized slitlamp optics and a visual acuity Snellen chart virtually projected at 20 ft. BCVA measurements were recorded, and biomicroscopic videos were scored for image quality of the anterior segment status on a scale from 1 to 5 (1 = poor and 5 = excellent) by a blinded observer. RESULTS: After a short instruction, all patients were able to self-image their eyes and perform a self-BCVA measurement using the e-Device. Patient self-image quality with the e-Device scored on average 3.3 (±0.8) for videos (n = 76) and 3.6 (±0.6) for photographs (n = 49). Self-BCVA measurement was within 1 Snellen line from routine BCVA levels in 66 of 72 eyes (92%). When compared with conventional biomicroscopy, patient self-biomicroscopy allowed for recognition of the relevant pathology (or absence thereof) in 26 of 35 eyes (74%); 9 cases showed insufficient image quality attributed to device operating error (n = 6) and mild corneal edema and/or scarring (n = 3). Patient satisfaction with the device was 4.4 (±0.9). CONCLUSIONS: An e-Device for combined BCVA self-measurement and biomicroscopy self-imaging may have potential as an aid in remote ophthalmic examination in the absence of an ophthalmic professional and may be considered for patients who are unable to visit an ophthalmic clinic for routine follow-up.