The dynamics of entropy in the COVID-19 outbreaks

With the unfolding of the COVID-19 pandemic, mathematical modelling of epidemics has been perceived and used as a central element in understanding, predicting, and governing the pandemic event. However, soon it became clear that long-term predictions were extremely challenging to address. In addition, it is still unclear which metric shall be used for a global description of the evolution of the outbreaks. Yet a robust modelling of pandemic dynamics and a consistent choice of the transmission metric is crucial for an in-depth understanding of the macroscopic phenomenology and better-informed mitigation strategies. In this study, we propose a Markovian stochastic framework designed for describing the evolution of entropy during the COVID-19 pandemic together with the instantaneous reproductive ratio. Then, we introduce and use entropy-based metrics of global transmission to measure the impact and the temporal evolution of a pandemic event. In the formulation of the model, the temporal evolution of the outbreak is modelled by an equation governing the probability distribution that describes a nonlinear Markov process of a statistically averaged individual, leading to a clear physical interpretation. The time-dependent parameters are formulated by adaptive basis functions, leading to a parsimonious representation. In addition, we provide a full Bayesian inversion scheme for calibration together with a coherent strategy to address data unreliability. The time evolution of the entropy rate, the absolute change in the system entropy, and the instantaneous reproductive ratio are natural and transparent outputs of this framework. The framework has the appealing property of being applicable to any compartmental epidemic model. As an illustration, we apply the proposed approach to a simple modification of the susceptible–exposed–infected–removed model. Applying the model to the Hubei region, South Korean, Italian, Spanish, German, and French COVID-19 datasets, we discover significant difference in the absolute change of entropy but highly regular trends for both the entropy evolution and the instantaneous reproductive ratio

Airborne DOAS measurements over the South African highveld

A thesis submitted to the Faculty of Geography, Archaeology, and Environmental Studies University of the Witwatersrand, Johannesburg, in fulfilment of the requirements of the degree of Doctor of Philosophy. 2015.An imaging DOAS instrument, along with in situ trace-gas and aerosol instrumentation was deployed on board a research aircraft over the Highveld region of South Africa, to make regional-scale measurements of nitrogen dioxide (NO2). The presence of a “hotspot” of NO2 over the Highveld is confirmed. Case-study estimates of NO2 emission flux were made downwind of a power station (10 tons.hr−1), a petrochemical plant (36 tons.hr−1) and the entire Highveld region (395 tons.hr−1). Vertical profile measurements were used to develop scenarios for a radiative transfer sensitivity study. From this, suitable air-mass factors for the DOAS measurements were determined. Comparisons between the airborne DOAS and satellite instruments show a good agreement where the spatial scales of the satellite ground pixels and the features in the two-dimensional trace-gas distribution are matched. A long-term record of satellite data was analysed. Analysis of radiative transfer revealed a possible artefact in the adjacent positive and negative trends evident on the Highveld. A correction to the satellite record for a seasonal bias was made, and found to be important over biomass burning regions in Angola and Zambia. Spatial features in a seasonal model of the satellite record are shown to correspond with known urban, industrial and biomass burning sources in the region. Signatures of soil emissions are also detected