COVID-19 and the maximum-entropy method : a study of its application in the estimation of the reproduction number

Abstract

In epidemic theory, the effective reproductive number describes the population-level spread of an infectious disease. It represents the average number of secondary cases generated for every primary infectious case. If R>1, the number of cases increases, contrariwise, if R<1 the number of cases falls. However, such a crucial parameter is brought to naught without good and substantial information. Furthermore, the COVID-19 pandemic has exposed deep-seated issues surrounding the quality of health data collection which have thus hampered the accuracy and availability of vital information. In statistical inference, the Maximum-Entropy Method, is a powerful tool used in the prediction of probability distributions, given a set of constraints. The probability distribution that is maximally noncommittal with regard to missing information, is considered to be the best that represents the current state of knowledge of the system. Ergo, solving the issue of incomplete information. This thesis therefore seeks to explore the viability of the Maximum-Entropy Method by first identifying the probability distribution of COVID-19 (given the mean and variance of the generation interval) to estimate the reproduction numbers, and subsequently implementing these values into a simple Susceptible-Infectious-Removed model (SIR) to plot an infections curve of the pandemic in Singapore, Japan, Israel, The UK and The US. For which, the simulations necessitate a time-varying generation interval parameter for the results to be in accordance with empirical data.