We consider a class of generalized nonlocal $p$-Laplacian equations. We find some proper structural conditions to establish a version of nonlocal Harnack inequalities of weak solutions to such nonlocal problems by using the expansion of positivity and energy estimates.

COVID-19 is causing a significant burden on medical and healthcare resources globally due to high numbers of hospitalisations and deaths recorded as the pandemic continues. This research aims to assess the effects of climate factors (i.e., daily average temperature and average relative humidity) on effective reproductive number of COVID-19 outbreak in Wuhan, China during the early stage of the outbreak. Our research showed that effective reproductive number of COVID-19 will increase by 7.6% (95% Confidence Interval: 5.4% ~ 9.8%) per 1°C drop in mean temperature at prior moving average of 0–8 days lag in Wuhan, China. Our results indicate temperature was negatively associated with COVID-19 transmissibility during early stages of the outbreak in Wuhan, suggesting temperature is likely to effect COVID-19 transmission. These results suggest increased precautions should be taken in the colder seasons to reduce COVID-19 transmission in the future, based on past success in controlling the pandemic in Wuhan, China.

Severe COVID-19 cases place immediate pressure on hospital resources. To assess this, we analysed survival duration in the first 39 fatal cases in Wuhan, China. Time from onset and hospitalization to death declined rapidly, from ~40 to 7 days, and ~25 to 4 days, respectively, in the outbreak’s first month.

This study explored how internet queries vary in facilitating monitoring of pertussis, and the effects of sociodemographic characteristics on such variation by city in Shandong province, China. We collected weekly pertussis notifications, Baidu Index (BI) data and yearly sociodemographic data at the city level between 1 January 2009 and 31 December 2017. Spearman's correlation was performed for temporal risk indices, generalised linear models and regression tree models were developed to identify the hierarchical effects and the threshold between sociodemographic factors and internet query data with pertussis surveillance. The BI was correlated with pertussis notifications, with a strongly spatial variation among cities in temporal risk indices (composite temporal risk metric (CTRM) range: 0.59–1.24). The percentage of urban population (relative risk (RR): 1.05, 95% confidence interval (CI) 1.03–1.07), the proportion of highly educated population (RR: 1.27, 95% CI 1.16–1.39) and the internet access rate (RR: 1.04, 95% CI 1.02–1.05) were correlated with CTRM. Higher RRs in the three identified sociodemographic factors were associated with higher stratified CTRM. The percentage of highly educated population was the most important determinant in the BI with pertussis surveillance. The findings may lead to spatially-specific criteria to inform development of an early warning system of pertussis infections using internet query data.

The plasma in the scrape-off layer (SOL) has an important effect on the coupling of the waves in the ion cyclotron range of frequencies (ICRF). The high-frequency B-dot (HFB) probes have been installed to investigate the behaviour of ICRF waves on EAST. The fast and slow ICRF wave field amplitudes are measured and a domain parallel wavenumber is deduced. Results of measurements on a test experimental platform and EAST experiments are presented, which include vacuum and plasma situations. In vacuum it is found that field amplitudes increase linearly with ICRF power. Besides, during plasma operation, field amplitudes measured were decreased by an order of magnitude and no linear relation with power was observed. Fast and slow wave power densities fluctuate strongly with plasma density. The experimental results in the laboratory coincide with the simulation results and allow for validating of the measurement method.