An SIR Model Including Asymptomatic Virus Carriers with Application

• 1、School of Mathematics and Physics, University of Science and Physics, Beijing 100083

Abstract： In December, 2019, a novel coronavirus-induced pneumonia (COVID-19) broke out in Wuhan, Hubei. To date, more than 300,000 people infected with COVID-19 have been identified. It affects more than 180 countries and regions on 6 continents except Antarctica. Establishing a mathematical model for epidemic infectious diseases has played an important role in the formulation, evaluation, and prevention of control strategies. One of the important factors for the rapid spread of COVID-19 is the presence of asymptomatic new coronavirus carriers. Based on the mathematical model of susceptible-infected-recoverer (SIR), a 4-variable differential equation model (NSIR) including asymptomatic virus carriers has been set up. The disease-free equilibrium point of NSIR was obtained. The discriminants of local stability and local unstability have been given. It gives discrimination of epidemic spread which related to disease transmission speed, cure rate and mortality rate, number of initial asymptomatic virus carriers, and number of initial infected individuals. Utilizing data from the Beijing New Coronavirus Pneumonia epidemic, first it was determined that the model parameters with different periods. Numerical simulation results show that the number of current infected COVID-19 individuals in Beijing will reduce to zero about mid-April; the death case was about 7 people. Second numerical simulation results estimate that if there were not prevention and control intervening, that is, implement a group immunity strategy, the number of infected COVID-19 individuals in Beijing will reach a peak in the mid-February, the infected cases are about 11.87 millions people. The further simulations show that the Beijing epidemic will end in the begin-November with death cases about 21,5000 people. Further more if implements loose prevention and control strategies, that is, only prevent and control infected individuals but not asymptomatic virus carriers. Then the Beijing epidemic will not end in the begin-November, and death cases will increase to about 20,0000 people. It seems that the whole nation's strict prevention and control strategies implemented in China are not only very effective but also completely necessary. Introduced the experimental and simulation of acute hepatitis B virus (HBV) infection in chimpanzees. It introduces the hypothesis that people are divided into 4 categories after virus infection. It points out the necessity of the current COVID-19 related prevention and control policy of the Chinese government. Medical staff in the intensive care unit of the COVID-19 intensive care unit are recommended to use face protection equipment similar to chemical soldiers. The research results can provide new theoretical tools and idea worthy of reference for better understanding and control of epidemic prevention and control.

Keywords： Epidemic and health statistics; new coronavirus; acute HBV infection; disease transmission; mathematical model; estimation of epidemic risk in Beijingord group immunity group immunity, loose immunity