Evolution model is based on that used by Hernandez et al., which considers the following groups: Susceptible, Incubating, Asymptomatic, Symptomatic, Hospitalized, Recovered and Accumulated deaths. Evolution model considers the possibility of infections from asymptomatic, symptomatic and hospitalized individuals. Evolution model considers the possibility that individuals who have recovered from the disease become symptomatic again. Observation model accounts for underreport of cases and deaths. Observation model accounts for delays in reporting cases and deaths. Model parameters were initially estimated with the Markov Chain Monte Carlo (MCMC) method, by using the data of the city of Rio de Janeiro from February 28, 2020 to April 29, 2020. These estimations were used as initial input values for the solution of the state estimation problem for the city of Rio de Janeiro. Algorithm of Liu & West for the Particle Filter was used for the solution of the state estimation problem because it allows the simultaneous estimation of state variables and model parameters. State estimation problem was solved with the data of the city of Rio de Janeiro, from February 28, 2020 to May 05, 2020. Monte Carlo simulations were run for 20 future days, considering uncertainties in the model parameters and state variables. Initial conditions were given by the state variables and corresponding distributions estimated with the particle filter on May 05, 2020. Distributions of the model parameters were also given by the estimations obtained for this date. Data of the city of Rio de Janeiro, from May 06, 2020 to May 15, 2020, were used for the validation of the solution of the state estimation problem. The present model, with the parameters obtained with the Particle Filter, accurately fits the number of reported cases and the number of reported deaths, for 10 days ahead of the period used for the solution of the state estimation problem. The Ratio of Infected Individuals per Reported Cases was around 15 on May 05, 2020. The Indexes of Under-Reported Cases and Deaths were around 12 and 2, respectively, on May 05, 2020. The Effective Reproduction Number was around 1.6 on February 28, 2020 and dropped to around 0.9 on May 05, 2020. However, uncertainties related to this parameter are large and the effective reproduction number is between 0.3 and 1.5, at the 95% credibility level. The particle filter must be used to periodically update the estimation of state variables and model parameters, so that future predictions can be made. Day 0 is February 28, 2020.
Globally Optimal Distributed Kalman Filtering for Multisensor Systems with Unknown Inputs
