A modified Susceptible-Infected-Recovered model for observed under-reported incidence data
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Fitting Susceptible-Infected-Recovered (SIR) models to incidence data is problematic when a fraction q of the infected individuals are not reported. Assuming an underlying SIR model with general but known distribution for the time to recovery, this paper derives the implied differential-integral equations for observed incidence data when a fixed fraction q of newly infected individuals are not observed. The parameters of the resulting system of differential equations are identifiable. Using these differential equations, we develop a stochastic model for the conditional distribution of current disease incidence given the entire past history of incidences. This results in an epidemic model that can track complex epidemic dynamics, such as outbreaks with multiple waves. We propose to estimate of model parameters using Bayesian Monte-Carlo Markov Chain sampling of the posterior distribution. We apply our model to estimate the infection rate and fraction of asymptomatic individuals for the current Coronavirus 2019 outbreak in eight countries in North and South America. Our analysis reveals that consistently, about 70-90% of infected individuals were not observed in the American outbreaks.
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