Abstract
A clear understanding of actual infection rate is imperative for control and prevention of diseases. In particular, it helps in formulating effective vaccination strategies and in assessing the level of herd immunity required to contain the virus. In this paper, we conduct theoretical and numerical study of a novel optimization procedure aimed at stable estimation of incidence reporting rate and time-dependent effective reproduction number from real data on new incidence cases, daily new deaths, and vaccination percentages. The iteratively regularized optimization algorithm can be applied to a broad class of data fitting problems constrained by various biological models, where one has to account for under-reporting of cases. To that end, general nonlinear observation operators in real Hilbert spaces are considered in the proposed convergence analysis. To illustrate theoretical findings, numerical simulations with SVIsIvRD compartmental model and real data for Delta variant of COVID-19 pandemic in different states of the US are conducted.
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