Differential equation analysis on COVID-19

Abstract

Background: An infectious disease caused by a novel coronavirus called COVID-19 has
raged 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 by
the epidemic. The deaths of many patients, including medical staff, caused social panic,
media attention, and high attention from governments and world organizations. Today, with
the joint efforts of the government, the doctors and all walks of life, the epidemic in Hubei
Province has been brought under control, preventing its spread from affecting the lives of the
people. Because of its rapid spread and serious consequences, this sudden novel coronary
pneumonia epidemic has become an important social hot spot event. Through the analysis of
the novel coronary pneumonia epidemic situation, we can also have a better understanding of
sudden 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 and
control model.
Methods: We establish different models according to the different developments of the
epidemic situation, different time points, and different response measures taken by the
government. To be specific, during the period of 2020.1.23-2020.2.7, the traditional SIR
model is adopted; during the period of 2020.2.8-2020.3.30, according to the scientific
research results, it was considered that the novel coronary pneumonia has a latent period, so
in 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, the
infected number, the cured number, death number and other factors, we simulate the change
of various numbers of people from the beginning to the next 180 days of novel coronary
pneumonia.
Findings: The results based on the analysis of differential equations and kinetic models show
that through the prediction of the model established in the first phase, the epidemic situation
of novel coronary pneumonia in Hubei Province was controlled at the end of March, which is
in line with the actual situation. The rest of Hubei province, except for Wuhan, lifted control
of the departure channel from 0:00 am on March 25, and Wuhan was also unblocked on April
8. Through the establishment of the second-phase model, it is found that the epidemic
situation will reach its peak in mid-February. For example, the quarantine admission of the
hospital declined after mid-February, which is inseparable from the measures to build square
cabin hospitals in early February so that more and more patients can be admitted. The model
established in the third phase shows that the epidemic had been completely controlled by the
end of May, which is also in line with the reality. Because in mid-May, the Wuhan
government conducted a nucleic acid test on all the citizens to screen for asymptomatic
infected persons to fundamentally control the spread of novel coronary pneumonia.
Interpretation: Hubei Province, as the center of the initial outbreak of novel coronary
pneumonia, people were forced to be isolated at home during the Spring Festival, the most
important Chinese holiday, and the whole society was in a state of suspension of work and
study. The Chinese government had taken many measures in response to the epidemic, such
as shutting down the city, vigorously building square cabin hospitals, and prohibiting people
from gathering. At the beginning of May this year, the epidemic in Hubei Province was
finally effectively controlled. For ordinary citizens, we should not cause unnecessary panic
about the unknown novel coronavirus. Instead, we should fully understand and be familiar
with this virus. In addition to the relevant medical knowledge, we should also understand the
spread of infectious diseases through appropriate mathematical models. By mathematical
models, we can understand the degree of harm of infectious diseases, when to control it, how
to stop it, and use scientific views to reveal the original face of the novel coronavirus to the
public without causing social panic