Analysis And Application Of Dynamics Modeling For Infectious Disease With Asymptomatic Infectious

The infectious diseases are the most serious diseases that still affect human health.The asymptomatic infection refers to an individual who is infected and does not show clinical symptoms until recovery.During this period,it will detoxify and can spread the infection.The asymptomatic infections cannot be identified and targeted for those with no symptoms.With the development of pathological studies of different infectious diseases,a large amount of evidence shows that many infectious diseases have the asymptomatic infectious,such as foot-and-mouth disease in animals and coronavirus(COVID-19)in humans.The asymptomatic infectious has an important impact on the spread and control of the infectious disease.There are three basic conditions of the infectious disease: susceptible populations sources of infection and transmission routes.The monitoring of the source has focused on the symptoms infectious.The infectious disease with the asymptomatic infectious can also affect the efficiency of interventions targeting susceptible individuals,such as vaccination.Because the serious implication of unknowingly the asymptomatic carriers is that it exerts selective pressure that may contribute to the emergence and transmission of drug-resistant strains.The asymptomatic infection is elusive nature and infectious,which is an important indicator of the existence of the virus and become the source of infection.At present,the relevant research results are mainly concentrated in medicine and public health and only a few focused on the theories.To provide the theoretical reference and the decision-making basis for the workers who take the prevention and control measures of infectious diseases,the quantitative and qualitative analysis of infectious diseases with asymptomatic infection is needed.Dynamic modeling is one of the most mature theories in the study of infectious diseases,which studies the occurrence development trend and distribution of the infectious diseases in the population.Through the computer simulation,the parameters are estimated and the risk factors for the spread are mined.In this paper,we construct some different dynamic models,which are used to analyze the influence of the asymptomatic infectious on the spread and control of infectious diseases,which includes the foot-and-mouth disease and COVID-19.Theoretically,the global asymptotic stability of equilibrium for the dynamic models is solved.In the application,the effective control measures of infectious diseases are put forward.Furthermore the works could also provide theoretical reference,decision-making basis and technical support for the prevention and control of other infectious diseases with the asymptomatic infectious.The main works and innovation points can be summed up as follows:(1)The epidemic of foot-and-mouth disease(FMD)remains particular concern in many countries or areas.In China’s mainland,the new cases of FMD decrease year by year through vaccination.However,a high antibody positive rate is found in the population by using the non-structural protein antibody detection method,there are asymptomatic infected animals in the population.We establish a dynamical model of FMD with two patches: within-farm and outside-farm.By constructing the Lyapunov function,we prove the equilibrium of the model are globally asymptotically.By carrying out the sensitivity analysis,we reach the conclusion that vaccination,quarantining or removing of the asymptomatic infectious animals and disinfection are the useful control measures for FMD at the large-scale cattle farm.(2)For analyze the transmission of the COVID-19 with the asymptomatic infections in region heavily affected within China in 2019.We present a dynamical model.Theoretically,we give the expression of the basic reproduction number,obtain the global dynamical behavior of the model.We use the traveller-derived cases in Anhui and Henan to quantify the spread of COVID-19 in Wuhan.The results showed that the larger the initial number of the asymptomatic infections is in the early days of the outbreak,the larger the final scale is.It is found that about 80 percent of Wuhan residents will eventually be infected without the control measures including the travel ban and the other measures,perhaps 80% of the people in Wuhan will be infected with COVID-19.The mass testing was taken at the end of the outbreak in Wuhan,the positive rate of the asymptomatic infection is 0.00303 / million.It shows that there are a large number of the asymptomatic infections.The extraordinary efforts implemented by China effectively contain the transmission of COVID-19 and protect public health in China.Especially,by the quarantine and medical observation,the risk of transmission of the asymptomatic infections is reduced.(3)To assess the effectiveness of mass testing and quarantine in the spread of COVID-19,we constructed a dynamic model with mass testing and quarantine.We proved the global stability of COVID-19 transmission via the Lyapunov function technique.We assessed the effectiveness of mass testing and quarantine.Sensitivity analysis indicated that the more people were tested per day,the larger the quarantine proportionality coefficient,the earlier the source location was determined,and the better the controlling effect.In addition,it was more effective to increase the coefficient of quarantine if the population density in the region was low.To eliminate the pandemic,the government has to expand testing and quarantine,requiring a large amount of continuous manpower,material,and financial resources.Therefore,new control measures should be developed.