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Real-world growth processes, such as epidemic growth, are inherently noisy, uncertain and often involve multiple growth phases. The logistic-sigmoid function has been suggested and applied in the domain of modelling such growth processes. However, existing definitions are limiting, as they do not consider growth as restricted in two-dimension. Additionally, as the number of growth phases increase, the modelling and estimation of logistic parameters becomes more cumbersome, requiring more complex tools and analysis. To remedy this, we introduce the nlogistic-sigmoid function as a compact, unified modern definition of logistic growth for modelling such real-world growth phenomena. Also, we introduce two characteristic metrics of the logistic-sigmoid curve that can give more robust projections on the state of the growth process in each dimension. Specifically, we apply this function to modelling the daily World Health Organization published COVID-19 time-series data of infection and death cases of the world and countries of the world to date. Our results demonstrate statistically significant goodness of fit greater than or equal to 99% for affected countries of the world exhibiting patterns of either single or multiple stages of the ongoing COVID-19 outbreak, such as the USA. Consequently, this modern logistic definition and its metrics, as a machine learning tool, can help to provide clearer and more robust monitoring and quantification of the ongoing pandemic growth process.