Establishment And Analysis Of Two Kinds Of Redpiratory Disease Models

Infectious disease dynamics modeling is the main content of biomathematics research.Combined with the knowledge of infectious disease dynamics,the reasonable establishment of disease model,combined with numerical simulation,the spread law of infectious disease,the analysis of the outbreak of infectious disease and the main causes of epidemic,to find the best method for prevention and control of infectious disease.The main research contents of this paper are as follows:The first part,according to the data provided by the Prevention and Control Center of Anhui Provincial Center for Disease Control and Prevention,statistical methods and relevant literature were used to find that PM_2.5has an impact on respiratory diseases.Therefore,this paper establishes a nonautonomous model of the transmission of respiratory diseases affected by air pollution,and fully takes into account the factors such as the increase of people's desire for prevention and control and the decrease of person-to-person transmission rate,without considering person-to-person transmission.The model was qualitatively analyzed with the knowledge of infectious disease dynamics,and the conditions for the persistence,extinction and global asymptotic stability of respiratory diseases were obtained.Based on the parameter estimation and numerical simulation of the number of respiratory clinics in Hefei,the effective incidence of people exposure to PM_2.5is 0.00000546.The second part,Since the first case of coronavirus disease(COVID-19)in Wuhan Hubei,China,was reported in December 2019,COVID-19 has spread rapidly across the country and overseas.The first case in Anhui,a province of China,was reported on January 10,2020.In the field of infectious diseases,modeling,evaluating and predicting the rate of disease transmission is very important for epidemic prevention and control.Different intervention measures have been implemented starting from different time nodes in the country and Anhui,the epidemic may be divided into three stages for January 10 to February 11,2020,namely.We adopted interrupted time series method and develop an SEI/QR model to analyse the data.Our results displayed that the lockdown of Wuhan implemented on January 23,2020 reduced the contact rate of epidemic transmission in Anhui province by48.37%,and centralized quarantine management policy for close contacts in Anhui reduced the contact rate by an additional 36.97%.At the same time,the estimated basic reproduction number gradually decreased from the initial 2.9764 to 0.8667and then to 0.5725.We conclude that the Wuhan lockdown and the centralized quarantine management policy in Anhui played a crucial role in the timely and effective mitigation of the epidemic in Anhui.One merit of this work is the adoption of morbidity data which may reflect the epidemic more accurately and promptly.Our estimated parameters are largely in line with the World Health Organization estimates and previous studies.