diff --git a/osspaper/paper.bib b/osspaper/paper.bib index fb8fcb4..4bd7f98 100644 --- a/osspaper/paper.bib +++ b/osspaper/paper.bib @@ -1185,7 +1185,7 @@ @article{ohnSmoothFunctionApproximation2019 } @article{okabeMathematicalModelEpidemics2020, - title = {A {{Mathematical Model}} of {{Epidemics}}\textemdash{{A Tutorial}} for {{Students}}}, + title = {A {{Mathematical Model}} of {{Epidemics}}---{{A Tutorial}} for {{Students}}}, author = {Okabe, Yutaka and Shudo, Akira}, year = {2020}, month = jul, diff --git a/osspaper/paper.md b/osspaper/paper.md index 11626e5..8b95041 100644 --- a/osspaper/paper.md +++ b/osspaper/paper.md @@ -33,7 +33,7 @@ model in Facebook's Prophet model for time-series growth-forecasting at scale [@taylorForecastingScale2018] on big data. The scientific basis for this prevalence is given in [@bejanConstructalLawOrigin2011]. Such growth-processes can be viewed as complex input--output systems that involve -multiple peak inflection phases with respect to time. An idea that +multiple peak inflection phases with respect to time, an idea that can be traced back in the crudest sense to [@reedSummationLogisticCurves1927]. A modern definition for the logistic-sigmoid growth which considers restricted growth from a two-dimensional perspective is the nlogistic-sigmoid function (`NLSIG`) [@somefunLogisticsigmoidNlogisticsigmoidModelling2020] or logistic neural-network (`LNN`) pipeline. @@ -43,37 +43,37 @@ of the COVID-19 epidemic growth in each affected country of the world and the wo # Statement of need -Admittedly, epidemiological models such as the SEIRD variants -[@leeEstimationCOVID19Spread2020;@okabeMathematicalModelEpidemics2020] are just another form of representing sigmoidal growth [@xsRichardsModelRevisited2012]. It has been noted in +Epidemiological models such as the SEIRD variants +[@leeEstimationCOVID19Spread2020;@okabeMathematicalModelEpidemics2020] are just another form of representing sigmoidal growth [@xsRichardsModelRevisited2012]. However, it has been noted [@christopoulosNovelApproachEstimating2020] that the SEIRD-variant models yield largely exaggerated forecasts. -Observing the current state of the COVID-19 pandemic, this is also true, as regards, +Observing the current state of the COVID-19 pandemic, this is concern is borne out, in the results of various applications of logistic modelling [@batistaEstimationStateCorona2020;@wuGeneralizedLogisticGrowth2020] -which have largely resulted in erroneous identification of the epidemic's progress and its future projection, hence leading policymakers astray [@matthewWhyModelingSpread2020]. +which have largely led to erroneous assessments of the epidemic's progress and its future projection, leading policymakers astray [@matthewWhyModelingSpread2020]. -Notably, two recurring limitations of the logistic definitions in the literature and other software packages exist. These two limitations are trends that have persisted since the first logistic-sigmoid function introduction [@bacaerVerhulstLogisticEquation2011]. +Notably, two recurring limitations of the logistic definitions in the literature and other software packages exist. These two limitations are trends that have persisted since the first introduction of the logistic-sigmoid function [@bacaerVerhulstLogisticEquation2011]. First is that, the co-domain of logistic function is assumed to be infinite. This assumption violates the natural principle of finite growth. Second is that, during optimization, estimation of the logistic hyper-parameters for the individual logistic-sigmoids that make the multiple logistic-sigmoid sum is computed separately, instead of as a unified function. The effect of this, is that, as the number of logistic-sigmoids -considered in the sum increases, regression analysis becomes more cumbersome and complicated as can be observed in these works [@leeEstimationCOVID19Spread2020;@batistaEstimationStateCorona2020; +considered in the sum increases, regression analysis becomes more cumbersome and complicated as can be observed in a number of works [@leeEstimationCOVID19Spread2020;@batistaEstimationStateCorona2020; @hsiehRealtimeForecastMultiphase2006;@wuGeneralizedLogisticGrowth2020; @chowellNovelSubepidemicModeling2019;@taylorForecastingScale2018]. -These limitations are efficiently overcome by the nlogistic-sigmoid function `NLSIG` (or logistic neural-network pipeline) for describing logistic growth. We note that the `NLSIG` is a logistic neural-network machine-learning tool under active development. The benefits it provides at a functional level: +These limitations are efficiently overcome by the nlogistic-sigmoid function `NLSIG` (or logistic neural-network pipeline) for describing logistic growth. We note that the `NLSIG` is a logistic neural-network machine-learning tool under active development. The benefits it provides at a functional level are: - - unified function definition + - unified function definition, - - functional simplicity and efficient computation + - functional simplicity and efficient computation, - - improved nonlinear modelling power + - improved nonlinear modelling power. -Ultimately, the development of the `NLSIG-COVID19Lab` was motivated by research needs, in that, it -illustrates the power of the nlogistic-sigmoid neural pipeline. `NLSIG-COVID19Lab` provides an optimization workflow with functions to make modelling and monitoring the COVID-19 pandemic easier and reliable. Notably, on the contrary, instead of engaging in false prophecy +Ultimately, the development of the `NLSIG-COVID19Lab` was motivated by research needs, in that it +illustrates the power of the nlogistic-sigmoid neural pipeline. \linebreak `NLSIG-COVID19Lab` provides an optimization workflow with functions to make modelling and monitoring the COVID-19 pandemic easier and reliable. Notably, instead of engaging in false prophecy or predictions on the cumulative growth of an ongoing growth phenomena, whose source is both uncertain and -complex to be encoded in current mathematical models [@christopoulosEfficientIdentificationInflection2016;@matthewWhyModelingSpread2020], this software package makes projections by means of: +complex to encode in current mathematical models [@christopoulosEfficientIdentificationInflection2016;@matthewWhyModelingSpread2020], this software package makes projections by means of: -- two-dimensional perspective metrics: Y-to-Inflection Ratio (YIR, Here Y = Infections or Deaths); X-to-Inflection Ratio (XIR, Here X = Time in Days) for robust monitoring of the growth-process being modelled in an area or locale of interest. +- two-dimensional perspective metrics: Y-to-Inflection Ratio (YIR, here Y = Infections or Deaths); X-to-Inflection Ratio (XIR, here X = Time in Days) for robust monitoring of the growth-process being modelled in an area or locale of interest, and -- adaptation of the Dvoretzky–Kiefer–Wolfowitz (DKW) inequality for the Kolmogorov–Smirnov (KS) test to construct a non-parametric confidence interval of uncertainty on the nlogistic-sigmoid model with a 99% probability ($\alpha=0.01$) by default. +- an adaptation of the Dvoretzky–Kiefer–Wolfowitz (DKW) inequality for the Kolmogorov–Smirnov (KS) test to construct a non-parametric confidence interval of uncertainty on the nlogistic-sigmoid model with a 99% probability ($\alpha=0.01$) by default. `NLSIG-COVID19Lab` is useful as a quick real-time monitoring tool for the COVID-19 pandemic. It was designed to be used by humans: both researchers and non-researchers. @@ -89,7 +89,7 @@ In this case, the growth-process is the time-series COVID-19 pandemic growth fro ### Core Data Source -As at the time of writing. The COVID-19 Database of `NLSIG-COVID19Lab` is sourced from the: +At the time of writing, the COVID-19 database of `NLSIG-COVID19Lab` is sourced from the: * World Health Organization @@ -116,7 +116,7 @@ and refer to \autoref{eq:fourier] from text. # Related research and software -To the best of knowledge, we are unaware of any other software packages or tool providing a similar purpose or functionality for describing the logistic growth of the COVID-19 pandemic from a realistic finite two-dimensional perspective of natural growth. +To the best of our knowledge, we are unaware of any other software packages or tool providing a similar purpose or functionality for describing the logistic growth of the COVID-19 pandemic from a realistic finite two-dimensional perspective of natural growth. This application of the `NLSIG` to modelling the COVID-19 pandemic was selected as the best paper at the *2nd African Symposium on Big Data, Analytics and Machine Intelligence and 6th TYAN International Thematic Workshop, December 3-4, 2020*. @@ -125,4 +125,4 @@ This application of the `NLSIG` to modelling the COVID-19 pandemic was selected This work received no funding. -# References \ No newline at end of file +# References