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Abstract A novel optimization algorithm for stable parameter estimation and forecasting from limited incidence data for an emerging outbreak is proposed.The algorithm combines a compartmental model of disease progression with iteratively regularized predictor-corrector numerical scheme aimed at the reconstruction of case reporting ratio, transmission rate, and effective reproduction number.The algorithm is illustrated with real data on COVID-19 pandemic in the states of Georgia and New York, USA.The techniques of functional data analysis are applied for uncertainty quantification in extracted parameters and in future projections of new cases. 

In the absence of reliable information about transmission mechanisms for emerging infectious diseases, simple phenomenological models could provide a starting point to assess the potential outcomes of unfolding public health emergencies, particularly when the epidemiological characteristics of the disease are poorly understood or subject to substantial uncertainty. In this study, we employ the modified Richards model to analyze the growth of an epidemic in terms of 1) the number of times cumulative cases double until the epidemic peaks and 2) the rate at which the intervals between consecutive doubling times increase during the early ascending stage of the outbreak. Our theoretical analysis of doubling times is combined with rigorous numerical simulations and uncertainty quantification using synthetic and real data for COVID-19 pandemic. The doubling-time approach allows to employ early epidemic data to differentiate between the most dangerous threats, which double in size many times over the intervals that are nearly invariant, and the least transmissible diseases, which double in size only a few times with doubling periods rapidly growing.

 

Simple mathematical tools are needed to quantify the threat posed by emerging and re-emerging infectious disease outbreaks using minimal data capturing the outbreak trajectory. Here we use mathematical analysis, simulation and COVID-19 epidemic data to demonstrate a novel approach to numerically and mathematically characterize the rate at which the doubling time of an epidemic is changing over time. For this purpose, we analyze the dynamics of epidemic doubling times during the initial epidemic stage, defined as the sequence of times at which the cumulative incidence doubles. We introduce new methodology to characterize epidemic threats by analyzing the evolution of epidemics as a function of (1) the number of times the epidemic doubles until the epidemic peak is reached and (2) the rate at which the doubling times increase. In our doubling-time approach, the most dangerous epidemic threats double in size many times and the doubling times change at a relatively low rate (e.g., doubling times remain nearly invariant) whereas the least transmissible threats double in size only a few times and the doubling times rapidly increases in the period of emergence. We derive analytical formulas and test and illustrate our methodology using synthetic and COVID-19 epidemic data. Our mathematical analysis demonstrates that the series of epidemic doubling times increase approximately according to an exponential function with a rate that quantifies the rate of change of the doubling times. Our analytic results are in excellent agreement with numerical results. Our methodology offers a simple and intuitive approach that relies on minimal outbreak trajectory data to characterize the threat posed by emerging and re-emerging infectious diseases. 

Abstract A parameter identification inverse problem in the form of nonlinear least squares is considered.In the lack of stability, the frozen iteratively regularized Gauss–Newton (FIRGN) algorithm is proposed and its convergence is justified under what we call a generalized normal solvability condition.The penalty term is constructed based on a semi-norm generated by a linear operator yielding a greater flexibility in the use of qualitative and quantitative a priori information available for each particular model.Unlike previously known theoretical results on the FIRGN method, our convergence analysis does not rely on any nonlinearity conditions and it is applicable to a large class of nonlinear operators.In our study, we leverage the nature of ill-posedness in order to establish convergence in the noise-free case.For noise contaminated data, we show that, at least theoretically, the process does not require a stopping rule and is no longer semi-convergent.Numerical simulations for a parameter estimation problem in epidemiology illustrate the efficiency of the algorithm.