A Theoretical Analysis of the COVID-19 Pandemic using a Public Database

This thesis investigates several issues (incubation and recovery periods, effect of lockdown, digital prognosis, prediction of new cases) of the pandemic COVID-19 based on mathematical models, computational methods and a publicly available database. Traditional compartment-based models have various partitions such as lockdown, susceptible, infected, confirmed cases, recovered, deaths, etc., with the inclusion of several model parameters. The first model is based on a set of coupled delay differential equations with fourteen delays to estimate the incubation period. The estimated mean incubation period we obtain is 6.74 days (95% Confidence Interval (CI): 6.35 to 7.13), and the 90th percentile is 11.64 days (95% CI: 11.22 to 12.17), which is a good agreement with statistical supported studies. The second model is a large-scale extension of the first model, including several hundred groups for recovered individuals and the death toll. This proposed model generates a new refined database of recovery as well as the death toll, the key source for studying recovery and decease periods. The estimated mean recovery period we obtain is 22.14 days (95% CI: 22.00 to 22.27), and the 90th percentile is 28.91 days (95% CI: 28.71 to 29.13), which is in agreement with statistical-supported studies. The third model is an extended SIRS model that includes lockdown as a model compartment. In addition, an electronic application has been developed that allows for a rapid digital prognosis of COVID-19 patients using the information, extracted from the publicly available database of Canadian patients. This tool aims to assist health specialists in their decision regarding COVID-19 patients, based on symptoms and age. Finally, a hybrid approach, a combination of neural networks, inverse problem and Taylor series expansion, based on a second order nonlinear differential equation for the total cases has been derived to forecast COVID-19 cases. The test results show that the proposed prediction model can forecast a range of 55 days.