The Evolution of the Identifiable Analysis of the COVID-19 Virus

Abstract

It is important to accurately forecast a new infection such as COVID-19 in order to effectively 4 implement control measures. For this purpose, we study whether the epidemiological parameters 5 such as the rate of infection, incubation period, and rate of recovery for the COVID-19 disease 6 can be identified from daily incidences and death data. The data are obtained from the Florida 7 Department of Health, which reports the numbers of daily COVID-19 cases and disease-induced 8 casualties. Two mathematical models that consist of a system of ordinary differential equations are 9 used to simulate the spread of the coronavirus in the Florida population. Structural identifiability 10 analysis is conducted on the models to determine whether the models are well-structured to forecast 11 the outbreak. Analysis revealed that the SEIR model is structurally identifiable, while the social 12 distancing model is not structurally identifiable. If the model is structurally unidentifiable, it may 13 not accurately forecast the pandemic, and in turn, may lead to inaccurate control measures. Then, 14 the practical identifiability of parameter estimates that provide the best fit was investigated using 15 Monte Carlo simulations. The practical identifiability analysis revealed that all of the parameters 16 in the SEIR model are practically identifiable, but the parameters δ, δE , and ρ were found to be 17 unidentifiable in the social distancing model. By comparing two models in this project, we were able 18 to determine the effectiveness of social distancing in preventing incidences and saving lives from the 19 disease in Florida. Furthermore, we consider how people’s behavior changes over time, and how this 20 may affect the rate of disease spread in the population. To represent this, we develop a recipe to 21 determine the time-dependent transmission rate, β(t), from the data and introduce a methodology 22 of how to accomplish this. 23