Dynamical Modelling And Analysis For Two Respiratory Infectious Diseases

The respiratory disease is a kind of disease transporting mainly by air,through the nasal cavity,larynx,trachea and bronchus,and finally causing all respiratory tracts above infected.Some pathogens among them such as scarlet fever and COVID-19,can even maintain certain infectious ability in the natural environment,which may cause infected cases,producing public panic.For the sake of scientific criteria for epidemic prevention and control,the thesis bases on its transporting traits,proposes and analyzes the correlative epidemic dynamical models,respectively.Here is the introduction for the thesis:Scarlet fever is an acute respiratory disease caused by bacteria,whose pathogens have a good capacity of living in natural surroundings.From 2011,the epidemic has a conspicuous tendency of resurgence globally.The paper,in the 2 section,proposes and analyzes the seasonal epidemic model and long time-scale endemic model to depict scarlet fever's short and long term behaviours,respectively.Firstly,the basic reproduction number(?)₀,epidemic peak and final size are calculated.If(?)₀>1,the epidemic will break out.The final size rises up monotonically with(?)₀increasing.In addition,the existence conditions of disease-free equilibrium and endemic equilibrium are investigated,and the relationships between the conditions and(?)₀are analyzed.Finally,through adding periodical coefficients,a numerical simulation is conducted according to the real datum of infection cases in China during 2011-2016,which implies the direct infection plays a critical role in the epidemic spread.COVID-19 is a severe infectious respiratory disease.The individuals infected by it can be classified into the exposed individuals and asymptomatic individuals.Its trans-mission channels contain direct infection by human to human and indirect infection by human to environment.According to the transporting groups and channels,the paper,in the 3 section,presents an epidemic model with multiple compartments and trans-porting channels.Through the model,the control reproduction number(?)₍(8)and basic reproduction number(?)₀are calculated;the epidemic peak,final size and duration time are studied;the outbreak threshold and estimation criteria are given.The model fits well with the real datum of infection cases in Heilongjiang China in April,2020.Fur-ther,the exposed individuals are the main transporting group;the direct infection is the main transporting channel;the asymptomatic individuals have a persistent influence on the epidemic spread,which probably is a potential hazard for epidemic prevention and control.