Differential equation analysis on COVID-19

Abstract

Background: An infectious disease caused by a novel coronavirus called COVID-19 hasraged across the world since December 2019. The novel coronavirus first appeared in Wuhan,China, and quickly spread to Asia and now many countries around the world are affected bythe epidemic. The deaths of many patients, including medical staff, caused social panic,media attention, and high attention from governments and world organizations. Today, withthe joint efforts of the government, the doctors and all walks of life, the epidemic in HubeiProvince has been brought under control, preventing its spread from affecting the lives of thepeople. Because of its rapid spread and serious consequences, this sudden novel coronarypneumonia epidemic has become an important social hot spot event. Through the analysis ofthe novel coronary pneumonia epidemic situation, we can also have a better understanding ofsudden infectious diseases in the future, so that we can take more effective response measures,establish a truly predictable and provide reliable and sufficient information for prevention andcontrol model.Methods: We establish different models according to the different developments of theepidemic situation, different time points, and different response measures taken by thegovernment. To be specific, during the period of 2020.1.23-2020.2.7, the traditional SIRmodel is adopted; during the period of 2020.2.8-2020.3.30, according to the scientificresearch results, it was considered that the novel coronary pneumonia has a latent period, soin the later phase of epidemic development, the government has effectively isolated patients,thus we adopt the SEIQR model accordingly. During the period of 2020.3.31-2020.5.16,because more asymptomatic infected people were found, we use the SEIQLR model to fit.Finally, through a SEIR simulator, considering the susceptible number, the latent number, theinfected number, the cured number, death number and other factors, we simulate the changeof various numbers of people from the beginning to the next 180 days of novel coronarypneumonia.Findings: The results based on the analysis of differential equations and kinetic models showthat through the prediction of the model established in the first phase, the epidemic situationof novel coronary pneumonia in Hubei Province was controlled at the end of March, which isin line with the actual situation. The rest of Hubei province, except for Wuhan, lifted controlof the departure channel from 0:00 am on March 25, and Wuhan was also unblocked on April8. Through the establishment of the second-phase model, it is found that the epidemicsituation will reach its peak in mid-February. For example, the quarantine admission of thehospital declined after mid-February, which is inseparable from the measures to build squarecabin hospitals in early February so that more and more patients can be admitted. The modelestablished in the third phase shows that the epidemic had been completely controlled by theend of May, which is also in line with the reality. Because in mid-May, the Wuhangovernment conducted a nucleic acid test on all the citizens to screen for asymptomaticinfected persons to fundamentally control the spread of novel coronary pneumonia.Interpretation: Hubei Province, as the center of the initial outbreak of novel coronarypneumonia, people were forced to be isolated at home during the Spring Festival, the mostimportant Chinese holiday, and the whole society was in a state of suspension of work andstudy. The Chinese government had taken many measures in response to the epidemic, suchas shutting down the city, vigorously building square cabin hospitals, and prohibiting peoplefrom gathering. At the beginning of May this year, the epidemic in Hubei Province wasfinally effectively controlled. For ordinary citizens, we should not cause unnecessary panicabout the unknown novel coronavirus. Instead, we should fully understand and be familiarwith this virus. In addition to the relevant medical knowledge, we should also understand thespread of infectious diseases through appropriate mathematical models. By mathematicalmodels, we can understand the degree of harm of infectious diseases, when to control it, howto stop it, and use scientific views to reveal the original face of the novel coronavirus to thepublic without causing social panic