# Improved Epidemic Dynamics Model and Its Prediction for COVID-19 in Italy
## 1 Introduction  
In December 2019, a new type of coronavirus pneumonia (COVID-19) broke out in Wuhan, China. Since then, there have been cases of infected individuals in various regions of the world. On 30 January 2020, the WHO listed COVID-19 as an \"emergency public health event of international concern\" [1]. According to the official statistics of the World Health Organization, as of 30 June 2020, the outbreak of COVID-19 has caused 10,193,723 confirmed cases and 503,867 fatalities globally [2]. The epidemic-prevention situation is extremely severe, and the number of confirmed cases in South Korea, Iran, the United States, and other countries continues to increase, while in Europe, Italy has become the \"severe disaster country\" of the epidemic. The collapse of the medical system [3] and the high proportion of the elderly population [4] make the mortality rate in Italy much higher than in other regions. According to the official report of the Italian Ministry of Health, as of 30 June 2020, the outbreak of COVID-19 has caused 240,578 confirmed cases and 34,767 fatalities in Italy, and the mortality rate is approximately 14% [5]. In view of the rapid spread of the epidemic nationwide, the Italian government took proactive prevention and control measures. On 10 March 2020, Italy implemented a lockdown measure nationwide. Scientific and effective calculation of the spread tendency of the epidemic is crucial to the decision on epidemic prevention and restriction. It should rely on theoretically perfect models, reasonable parameters, and accurate predictions. The mathematical models generally advocated to describe the spread of infectious diseases include the Susceptible-Infectious-Recovered model (the SIR model), Susceptible-Exposed-Infectious-Recovered model (the SEIR model),and Susceptible-Infectious-Diagnosed-Recovered model (the SEIJR model). The main idea is to divide the population into groups such as susceptible, latent, infectious, diagnosed, and recovered ones. We have established differential equations according to the propagation mechanism among various groups and then revealed the spreading laws of the epidemic. The dynamic model is modeled according to the transmission of disease, and the model is interpretable and expandable. Game theory continues to be an effective tool to model intervention decision making by individuals [6]. [PERSON] et al. used game theory to introduce the decision making of individuals into the SIR model and then get the effect of the vaccination on the epidemic [7]. Over the years, numerous research projects and promotions have been built on the original SIR model to meet different epidemic characteristics. As the global epidemic becomes more severe, a more complete infectious-disease model is urgently needed. Many scholars have adopted the infectious-disease-dynamics model for COVID-19 [8; 9; 10; 11; 12; 13; 14]. Based on the traditional SEIR model, the population is divided more concretely. Here, we will briefly review the following articles. The recent work of [PERSON] et al. [8] proposed a deterministic compartment model containing isolation measures and epidemiological conditions, but this model implied that the latent patients are not infectious and therefore does not reflect the dynamics of COVID-19. [PERSON] et al. [9] proposed an infectious-disease-dynamics model based on the time-delay dynamic system, which introduced the time-delayed processes of incubation, recovery, and fatality. However, they did not consider the different types of infected people (symptomatic or asymptomatic), and the definition of patients during the infectious incubation period was not clear. [PERSON] et al. [10] considered traffic factors based on the traditional SEIR model and predicted the number of total cases imported from Wuhan, China, but they did not explicitly consider the impact of quarantine measures in the dynamic. [PERSON] et al. [11] presented an improved epidemic-dynamics model.