COVID-19 Spread Model in Hubei Province

This article provides prognosis of COVID-19 spread in Chinese province Hubei from January 22 2020 using SIR model. To compare the results with real data, we use statistics obtained by Johns Hopkins University.


Introduction
Pandemics are large-scale outbreaks of infectious disease that can greatly increase morbidity and mortality over a wide geographic area and cause significant economic, social, and political disruption. Evidence suggests that the likelihood of pandemics has increased over the past century because of increased global travel and integration, urbanization, changes in land use, and greater exploitation of the natural environment [1]. First detected in Wuhan, China, in December 2019, the Coronavirus Disease (COVID-19) had rapidly spread by late January 2020 to all Chinese provinces and many other countries. On January 30, 2020, the World Health Organization (WHO) issued a Public Health Emergency of International Concern (PHEIC) and on March 11th, the WHO declared a pandemic for the COVID-19. By April 6, 2020, the virus had affected more than 1,200,000 people and caused the deaths of 70,000 in more than 180 countries [2].
It is critically important to predict count of infected people and death cases through the pandemic. There are plenty models to use them for different tasks . In our work we apply standard susceptible-infected-recovered (SIR) model that has more advantages and provides better results than susceptible-infected (SI) model [27]. A feature of diseases such as influenza and those caused by coronaviruses such as SARS, MERS and COVID-19, is that individuals practice social distancing to reduce the contact rate [28], so quarantine factor is implemented in our model, providing more flexibility and letting to control peak of disease. In the SIR model individuals are classified as Susceptibles (S), Infected (I) or Recovered (R), and that the only possible transitions are S → I (new infection) and I → R (recovery with permanent immunity). Also that model does not consider new births or deaths (other than because of the disease), so it is appropriate for an epidemic that develops on a time-scale much faster than demographic turn-around [29].
Resent researches show that Covid-19 activity hardly disappears completely [30]. Even with very strong restrictions in Wuhan, it stayed on an intermediate level for several days, and then went down to almost zero. To describe the global Covid-19 spread, Johns Hopkins University established database of cumulated numbers of confirmed cases, deaths and recoveries, for each day and each 3 on countries to prepare hospitals, protect medical workers, and decide on the need for social exclusion measures.
As of April 16, 2,084,049 cases of infection were confirmed in 210 countries and territories, 134,669 deaths, 515,147 recovered, mortality from all registered completed cases of infection is 21%. The regions most affected by the pandemic in terms of the number of cases are the USA, Europe (Italy, Spain, Germany, France, Great Britain), China, Iran. The number of cases of infection can be greatly underestimated -first of all, due to those who have a mild illness. Some countries (for example, Italy and Switzerland) have a policy of not testing people who have only minor symptoms of the disease [35].
There is no specific antiviral therapy against SARS-CoV-2 virus and there is no evidence of effective immunomodulating. Antibiotics against viruses are useless and are not used in treatment. However, they can be prescribed if a bacterial secondary infection is detected. Basically, patients receive symptomatic and supportive therapy. In severe cases, treatment is aimed at maintaining the vital functions of the organs.
COVID-19 and influenza are similar in clinical manifestations of the disease: infections can be asymptomatic, mild or severe, including with a risk of death. Both diseases can cause pneumonia. The viruses that cause both diseases are also transmitted in a similar way: by contact, by airborne droplets, in particular through an aerosol, and through objects or surfaces.
However, the flu has a shorter incubation period (about 3 days), due to which it spreads faster. Moreover, unlike COVID-19, the transmission of influenza viruses occurs to a greater extent until the onset of symptoms. In the case of influenza, the spread is mainly due to children, while COVID-19 affects mainly adults, from whom children are already infected, based on an analysis of cases of diseases among families in China.
With influenza, the percentage of severe and critical cases of the disease is also less. Mortality due to COVID-19 is probably higher than in the case of seasonal flu, in which it is 0.1%. In the case of influenza, children and older people are most at risk, while in the case of COVID-19, current data show that the risk is greater among older people and people with chronic diseases [36].
According to virologists from the UK and Germany, a pandemic can last from one to two years. American epidemiologist professor Justin Lelsler believes that COVID-19, on the one hand, will not disappear, and on the other, it will not become an obstacle to the normalization of life, which will come about thanks to vaccines or due to the population gaining immunity in a natural way.
Employees at Johns Hopkins University conducted a computer simulation of the development of the pandemic, based on which a forecast was compiled for different countries, provided that the antiepidemic measures are maintained or introduced. According to this forecast, quarantine measures in most countries can be canceled no earlier than August -September 2020.
Morgan Stanley analysts analyzed the situation and released a report for the United States, in which the first wave of patients will go to work in early June 2020, the second in August, and schools will open by October 2020. They predict the emergence of an experimental vaccine and its use for vaccinating medical personnel in November 2020, and mass vaccination in the spring of 2021.
Of great importance in understanding the mechanisms of the spread of the disease is the stability of the virus in the environment. So on different surfaces it is different and depends on temperature and humidity at +22 ° C and humidity of 65%. on paper, the virus is destroyed in 3 hours, on banknotes in 4 days, on wood and clothes in 2 days, on glass in 4 days, on metal and plastic in 7 days. Testing was carried out by PCR test, that is, it was not the time required to deactivate the virus, but its complete destruction -before the destruction of all copies of its RNA. In the external environment, coronoviruses are usually inactivated from surfaces at +33 ° C in 16 hours, at +56 ° C in 10 minutes.
For the pathogen COVID-19, special studies have established that it is stable at a temperature of +4 ° C. At this temperature, the virus is destroyed very slowly and even after 14 days the PCR test detects the whole genome of the virus. At room temperature around +22 ° C, the PCR test detects the virus according to the genome within a week, and after 14 days the virus is completely destroyed to RNA. The sensitivity of coronaviruses to ultraviolet radiation from the Sun and an increase in temperature 4 makes them seasonal diseases, but a significant factor is the combination of temperature with humidity and the angle of incidence of sunlight, which allows you to specify cities with an unfavorable climate where a surge in the incidence of coronaviruses can be expected. A study by American scientists found that large cities with a climate conducive to the spread of coronaviruses include: London, New York, Warsaw, Kiev, Berlin, Prague. In these cities, infectious disease specialists predict a surge in the COVID-19 pandemic due to favorable climatic conditions for coronaviruses.
All means of processing the hands within 30 seconds destroyed the virus below the detection threshold. Thus, the use of hand sanitizers is effective against coronaviruses. WHO recommends the use of alcohol-containing antiseptics against coronaviruses. Also, WHO notes that thorough washing of hands with soap is effective against coronaviruses, since viruses are effectively washed off the skin mechanically [37].
COVID-19 is anthropozoonosis (only in 1% of cases is transmitted from animals to humans) The transmission mechanism is aerogenic (through air); transmission methods airborne, airborne dust, contact-household, possibly fecal-oral (6% found in feces, 6% in urine) Infectious rate 2-3 Coronavirus SARS-CoV-2 has the largest non-segmented RNA, that is, it has the most complicated structure of all known viruses. The corona-shaped teeth on its surface carry fake (false) proteins at the end, which are captured by the receptors for angiotensin-converting enzyme 2 on the wall of the target cell and through the transmembrane protein penetrate into the cell, the virus replicates and exocytoses it, accompanied by cell death. The mechanism is the same as that of SARS-CoV.
The incubation period is usually about 5 days, but can last from 2 to 14 days in rare cases, up to 24. The disease becomes contagious before the onset of symptoms. A distinctive feature of the current pandemic, which makes it difficult to combat it, is a long incubation period. Another adverse feature is the large number of asymptomatic patients, that is, individuals who, having become infected with a coronavirus infection, do not show clinical manifestations, although they are able to infect others [13].
The main symptoms are [39] : fever -89%, cough-68%, diarrhea -4%, vomiting -5%. Complications: Among the complications, viral pneumonia is leading. Deterioration in viral pneumonia is proceeding rapidly, and many patients have already developed respiratory failure within 24 hours, requiring immediate respiratory support with mechanical ventilation. Quickly started treatment helps to alleviate the severity of the disease.
Mortality among completed cases is 20%. Death occurs against the background of viral lung damage and the development of acute respiratory distress syndrome. Effective etiotropic treatment to date does not exist. Non-specific prophylaxis. The vaccine is being developed and the probable time of occurrence is autumn 2020.

The SIR model
In this work we use standard SIR model with some changes.
One day was taken as the unit of time and one thousand people as unit of measurement of quantities. As initial conditions we use data for January 22: 0 = 58000, 0 = 0.444, 0 = 0.017, 0 = 0, 0 = 0.028

Results
The following are the simulation results with the selected parameters.

Conclusion
In this work we constructed model that predicts spread of COVID-19 from January 22 in Hubei. As it may be seen from the graphs peak of disease is already over. However, it will totally disappear not earlier than start of June. It shows that even province where quarantine was implemented first is still in danger. Also it is worth mentioning that the number of deaths almost stopped growing. It shows how quarantine factor may be important in large pandemics such as COVID-19.