Dynamic Analysis Of Influenza And COVID-19 Transmission Models

The recurrence of infectious diseases(such as influenza A,H1N1)and new infectious diseases(Corona Virus Disease 2019,COVID-19)threaten people’s life and health.In 2009,the United States experienced a large-scale outbreak of influenza A(H1N1),infecting more than 200 countries and regions,with nearly 200000 deaths.Although the pandemic period of influenza has ended,it still has a significant impact on human life.Due to people’s irrational use of drugs and long-term use of drugs,the body develops certain resistance to drugs,developing drug resistance,which greatly reduces the efficacy of drugs against the influenza virus(H1N1),Therefore,the study of drug resistant strains is still of great significance for disease prevention and control.At the end of December 2019,the newly emerging infectious disease COVID-19 began to propagate worldwide,causing a significant impact on global public health.With the emergence of a large number of asymptomatic infections and mutant strains,the difficulty of epidemic prevention and control has greatly increased.Based on the transmission mechanism of H1N1 influenza and COVID-19,this paper establishes three mathematical models of infectious diseases,analyzes their dynamic properties,and estimates parameters using statistical analysis methods such as ordinary least squares,in order to conduct numerical simulations to study the main factors affecting disease transmission.The main content includes the following three aspects:Part Ⅰ:Based on the transmission mechanism of influenza A(H1N1),anSVEI_S I_R R infectious disease model is constructed.Firstly,the control reproduction number_cR with vaccination measure is calculated,and the existence of endemic disease equilibrium is proved whenR_c>1;whenR_c<1,the global stability of the disease-free equilibrium is proved.Secondly,sensitivity analysis is conducted on parameters using the Sobol method,and finally numerical simulations are proceeded.The results show that the size of infection decreased with the increase in the self healing rate of latent infections 1-p;besides that,treatment rate f and vaccination rateηhave a crucial impact on the reduction in the number of infections.Therefore,medical advice should be followed to prevent drug abuse and increase the vaccination rate.Part Ⅱ:According to the transmission characteristics of COVID-19,considering the addition of compartments to isolate people infected in the incubation period in the model.The control reproduction numberR_c,the proof of the global stability of the disease-free equilibrium and the existence of the endemic disease equilibrium are carried out for the model.And sensitivity analysis is conducted on the main parameters of the model:the isolation rate of susceptible and latent infected individuals.The fitting effect of the model is verified using the data of the Indian epidemic situation,and predicted the development trend of the epidemic.In addition,the numerical simulation results indicate that:(1)increase the detection of latent infected individuals and increase their isolation rate;(2)susceptible individuals should strengthen their sense of self isolation.These two measures can greatly slow down the spread of the epidemic and reduce the size of infected individuals during the outbreak.Part Ⅲ:Based on the transmission mechanism of COVID-19 in Shanghai in April 2022,the chapter establish an SVEAIQR infectious disease model to study the impact of media coverage and vaccination on the spread of COVID-19,and fit the force of infection,isolation rate,vaccine efficiencyεand other important parameters based on the data from the Shanghai Municipal Health Commission and the National Health Commission of the People’s Republic of China.At the same time,the control reproduction number and the final size are calculated.In addition,through the sensitivity analysis of PRCC(partial rank correlation coefficient),we discuss the influence of the behavior change constant k reported by the media and vaccine efficiency on the transmission of COVID-19.Numerical studies have shown that improving media coverage,vaccination,and vaccine efficiency have a very positive effect on reducing the number of COVID-19 infections during an outbreak.