Before the lock-down of Wuhan/Hubei/China, on January 23 rd 2020, a large number of individuals infected by COVID-19 moved from the epicenter Wuhan and the Hubei province due to the Spring Festival, resulting in an epidemic in the other provinces including the Shaanxi province. The epidemic scale in Shaanxi was comparatively small and with half of cases being imported from the epicenter. Based on the complete epidemic data including the symptom onset time and transmission chains, we calculate the control reproduction number (1.48-1.69) in Xi'an. We could also compute the time transition, for each imported or local case, from the latent, to infected, to hospitalized compartment, as well as the effective reproduction number. This calculation enables us to revise our early deterministic transmission model to a stochastic discrete epidemic model with case importation and parameterize it. Our model-based analyses reveal that the newly generated infections decay to zero quickly; the cumulative number of case-driven quarantined individuals via contact tracing stabilize at a manageable level, indicating that the intervention strategies implemented in the Shaanxi province have been effective. Risk analyses, important for the consideration of "resumption of work", show that a large second outbreak is expected if the level of case importation remains at the same level as between January 10 th and February 4 th 2020. However, if the case importation decreases by 30%, 60% and 90%, the second outbreak if happening will be of small-scale assuming contact tracing and quarantine/isolation remain as effective as before. Finally, we consider the effects of intermittent inflow with a Poisson distribution on the likelihood of multiple outbreaks. We believe the developed methodology and stochastic model provide an important model framework for the evaluation of revising travel restriction rules in the consideration of resuming social-economic activities while managing the disease control with potential case importation.

The epidemic of novel coronavirus pneumonia has spread throughout the country. The early epidemic cases in many provinces, including Shaanxi, are mainly imported cases. The latest epidemic situation has been decreasing under restrict prevention and control strategies. Accessing the efficacy of control measures, analyzing the impact of population flow on the epidemic situation are of great significance for the study of the epidemic situation in Shaanxi (or other areas with imported cases as the main cases) and the future response to emergent infectious diseases. According to the detailed data published by Shaanxi, we can obtain the transmission chains (infection tree), and the median durations from the illness onset to the first medical visit, to the admission, and then to the final confirmation. We can obtain the daily number of latent, infectious and hospitalized individuals and the spatial distribution of their state evolution. The control reproduction number of COVID-19 epidemic was determined (1.48-1.69). We develop the statistical inference method to calculate the effective regeneration number under the strict control measures in Shaanxi province. Furthermore, a novel stochastic discrete transmission model for COVID-19 was proposed, which integrates possible interventions and import cases. The parameterization of the formulated model was realized through multiple source data. Our main conclusion shows that intermittent population flow, close attention and effective isolation of the floating population can effectively reduce the risk of secondary outbreak, which consequently provides decision support for the orderly organization of returning to work/school.

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Although many mathematical methods were used to analyze the neural activity under sinusoidal stimulation within linear response range in vestibular system, the reliabilities of these methods are still not reported, especially in nonlinear response range. Here we chose nonlinear least-squares algorithm (NLSA) with sinusoidal model to analyze the neural response of semicircular canal neurons (SCNs) during sinusoidal rotational stimulation (SRS) over a nonlinear response range. Our aim was to acquire a reliable mathematical method for data analysis under SRS in vestibular system. Our data indicated that the reliability of this method in an entire SCNs population was quite satisfactory. However, the reliability was strongly negatively depended on the neural discharge regularity. In addition, stimulation parameters were the vital impact factors influencing the reliability. The frequency had a significant negative effect but the amplitude had a conspicuous positive effect on the reliability. Thus, NLSA with sinusoidal model resulted a reliable mathematical tool for data analysis of neural response activity under SRS in vestibular system and more suitable for those under the stimulation with low frequency but high amplitude, suggesting that this method can be used in nonlinear response range. This method broke out of the restriction of neural activity analysis under nonlinear response range and provided a solid foundation for future study in nonlinear response range in vestibular system.