# Improved Epidemic Dynamics Model and Its Prediction for COVID-19 in Italy
## 4 Empirical Analysis  
1. Fitting Effect: Based on the cumulative number of confirmed cases in Italy as of 30 June 2020, we used the SEIR_QJD model for data fitting. The fitting effect of the model is measured by calculating the average deviation between the actual and simulated cumulative number of confirmed cases (Table 2). The curve fitting of Italian epidemic cases is shown in Figure 5. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameter** & **Definitions** & **Search Range** & **Estimated Mean Value** \\ \hline \(c_{1}\) & Adjustment coefficient of \(\beta\) with the government’s lockdown measures & 0.20 \(\sim\) 0.80 & 0.3068 \\ \(c_{2}\) & Adjustment coefficient of \(\beta\) with the government lifting the blockade & 1.00 \(\sim\) 2.00 & 1.0949 \\ \(w_{l}\) & The infectiousness of symptomatic & 2.0 & 2.0[12] \\  & individuals relative to incubation ones & & \\  & The speed of individuals from exposed & & \\ \(\lambda\) & to infected, which is the reciprocal of & 1/5.3 & 1/5.9 \\  & the incubation period & & \\ \(\rho\) & The proportion of asymptomatic & 0.10 \(\sim\) 0.60 & 0.4099 \\  & individuals among all infected ones & & \\ \(\alpha\) & The diagnosed speed of & 0.0 \(\sim\) 0.5 & 0.0788 \\  & symptomatic individuals & & \\ \(\gamma_{A}\gamma_{l}\) & The recovery rate of & 0.1 & 0.1[9] \\  & infected individuals & & \\  & The recovery rate of & 0.01887 & 0.01887 \\ \(\gamma_{l}\) & diagnosed individuals & & \\ \(\delta_{l},\delta_{l}\) & The mortality rate of infected and & \(f(t)\) & \(f(t)\) \\  & diagnosed individuals & & \\ \hline \hline \end{tabular}
\end{table} 
Table 1: _Cont._  
Figure 5: Simulation of epidemic-situation development trend. Simulation of the epidemic spread in Italy. Fitting curves: cumulative incidence (**a**), prevalence (**b**), incidence (**c**). This paper evaluates the fitting effect of the model by calculating the deviation between the simulated value and the real value (Table 2). The average deviation of the model in the past 90 days was 0.86%, and the maximum deviation was controlled within 2.95%. Overall, the fitting effect of the model was very good and, to a great extent, largely simulated the development of the Italian epidemic. 2. The duration of the epidemic is relatively long. With the change in government control, people's awareness of epidemic prevention, medical level, and other factors, the contact rate between susceptible and infected people will also change accordingly. This paper describes the change by constructing a time-varying function of the contact rate. During the implementation of the nationwide \"lockdown measures\" in Italy, the time-varying parameters changed significantly (adjustment coefficient c_1 was 0.4364), while after the closure measures, the change of time-varying parameters was insignificant, indicating that the epidemic situation in Italy was basically under control and there was no secondary outbreak. Furthermore, according to the model (1-8), we used the regeneration matrix to get the formula of the regeneration number:  
\[R_{c}=[\frac{\beta(1-\rho)w_{I}(1-l)}{\delta_{I}+\gamma_{I}+a}+\frac{\beta \rho w_{A}(1-l)}{\gamma_{A}}+\frac{\beta(1-l)}{\lambda}]S_{0} \tag{10}\]  
The regeneration numbers of the three stages were \(R_{c0}=2.9527\), \(R_{c1}=0.7064\), and \(R_{c2}=0.8204\), respectively, indicating that the government's prevention and control measures suppressed the spread of the epidemic effectively. 3. COVID-19 is a disease with strong spreading ability, which can be effectively controlled under good public health conditions and quarantine measures. In order to analyze the impact of the government's response on the epidemic, this paper simulates four different situations by changing the time of the government interventions, which is based on time-varying parameters (Figure 6). The analysis showed that the government's timely intervention measures could reduce the scale of the disease significantly.