Data sources and assumptions
The actual epidemic data used in this article comes from the official website of Chinese Center for Disease Control (Http://2019ncov.chinacdc.cn/2019-nCoV/) and Prevention and Hubei Provincial Health Commission Epidemic situation notification data (Http://wjw.hubei.gov.cn/). It was reported that the first COVID-19 case identified first exhibited symptoms on 12/08/2019. We assume that the patient was infected on 12/1/2019, one incubation period earlier than the onset date, and 12/1/2019 was set as day 0 of the simulation. The epidemic data from December 1, 2019 to April 25, 2020 were taken for research.
According to the current monitoring data and research, the epidemiological and clinic characters of Covid-19 are as follows: (1) The incubation period of the disease is contagious18,19. (2) Asymptomatic infected persons are contagious, but the length of the contagion period, the strength, and pathway of transmission need to be further studied20. (3) According to "novel coronavirus Diagnosis and Treatment Plan (Trial Seventh Edition)", infected population is divided into mild, common, heavy and critical types21,22. With the surge of infections placed huge pressure on the city’s medical system, thousands of light and common patients with COVID-19 had to be sent home for isolation and observation.
On the 55th to 60th days after the first case, the government took a series of measures to prevent the spread of the epidemic. On January 23, Wuhan City announced the "closure of the city", the contact rate between personnel is relatively stable. On January 28, Wuhan Fangcang hospitals were established to isolate and treat lightly infected persons. From this moment, all confirmed patients, including mild patients have truly achieved institutional isolation.
According to the official National Bureau of Statistics, the demographic data for 2018 published on the website (http://data.stats.gov.cn) set the permanent population of Hubei Province to 11 million.
Modified SEIR Model
The Susceptible-Exposed-Infectious-Removed (SEIR) model is a compartmental model for modeling how a disease spreads through a population. It’s an acronym for Susceptible, Exposed, Infected, Recovered. The model assumes that all individuals in the population have the probability of being infected. When a disease is introduced to a population, the people move from one of these classes (or compartments) to the next. When they reach the R state, they’re no longer able to be infected, they either survived the disease and are now immune or succumbed to the illness and are out of the population.
The modified SEIR Model in the present study is a stochastic SEIR model, it further expanded on the basis of the SEIR model to increase isolated exposed by tracking close contacts (Eq), untreated asymptomatic patients (Iq), untreated severe patients (Is), untreated normal patients (In), untreated mild patients (Im), untreated asymptomatic patients (Ia), quarantine or treated in any kinds of care facility (Qhospital), quarantine or treated in community or home (Qcommunity). The conversion relationship of different types of population is shown in Figure 1.
The setting of parameters in the model is combined with epidemiological investigations, published literatures, official news releases, and expert opinions. The unknown parameters are estimated using the software's built-in optimizer, the loss function is set to minimize the root mean square error (RMSE), and iteratively solved by the Gradient descent algorithm.
Three scenarios were set during the simulation:
- Scenario 1: With all mitigation measures that taken placed in Wuhan: using Fangcang hospital to treat and isolate all mild or asymptomatic patients in care facilities, building temporary designated hospital, city lockdown, social distancing, people stay at home, strong surveillance in community, people highly compliance to the prevention and control measures. Set all available parameters to simulate the epidemic trends of cumulative confirm cases, cumulative death cases and daily new cases that can fit the curves of Wuhan. This scenario will be used as a baseline compare with the other scenarios.
- Scenario 2: What if no Fangcang shelter hospitals were used and during the epidemic period. Mild patients who were treated in Fangcang shelter hospitals in the past must be isolated at home with other mitigation measures still implemented in community.
- Scenario 3: What if no strict management on mild patients. No Fangcang hospital, no strong surveillance in community, people have lower compliance to the prevention and control measures.
When performing analysis of a certain research scenario, the parameters in the model will give its probability distribution or range of assumptions according to the literature. Through the Monte Carlo (MCMC) algorithm, iterate iteratively 1000 times, the ranges of simulation results are used to achieve a robust estimate of the scenario.
The model is built with Anylogic Professional version 8.5.2. Through the event trigger mechanism in the software, the model parameters are dynamically adjusted at a specific time point to simulate the implementation of specific prevention and control measures.
The parameters for building the model are listed in Table 2 and 3. Notations in the model are listed in Table 1. The R0 value of COVID-19 has been calculated based on earlier data is reported in the range 1.4-3.9. The incubation period of the disease is generally 3-7 days, the shortest incubation period is one day, and the longest incubation period is 14 days.