Modeling COVID-19: Forecasting and analyzing the dynamics of the outbreak in Hubei and Turkey

ibrahim Halil Aslan; Mahir Demir; Michael Morgan Wise; Suzanne Lenhart

In the part, we fit the model (1) with available COVID-19 data from Turkey ((Ministry of Health (Turkey), 2020)). We fit the model (1) with Turkish data from March 10, 2020 to April 10, 2020, and get about 5.9% relative error in the fit by using the equation (3). We estimate the four parameters i q , s q , β, and r, which are not only the most significant parameters in the dynamics of outbreak, but also are specific to each country since they are related to the number of COVID-19 tests administered i q , the number of individuals in quarantine s q , the contact rate of individuals β, and the efficiency of quarantine r in each country. Therefore, by using the initial conditions: S(0) = 83, 000, 000, S q (0) = 0, I q (0) = 1, and R(0) = 0, we estimate these four parameters together with the initial number of exposed and infected individuals. We do not estimate the rest of the parameters, employing the parameters in Table 1 . Therefore, our results in this section will depend on observed dynamics of the outbreak in Hubei as well as the available Turkish data (((Ministry of Health (Turkey), 2020)). Note that the quarantine rate and the rate of reported cases (which, we stress, is related to number of COVID-19 tests) can be increased, and the increase still may have significant effect toward the reduction of the number of cases (See Figure 6 , sensitivity analysis), but increasing the reduction rate r does not make very significant changes by way of the number of cases in Turkey since it is very close to its maximum level (See Figure 6 , sensitivity analysis part). Thus, we will vary only the quarantine rate s q and the rate of reported cases i q in forecasting the peak of the outbreak and the number of cases/deaths in Turkey.