Research Of An Avian Influenza A (H7N9) Epidemic Model With Limited Hospital Resources

Human infections by H7N9 virus had not previously been reported until it was found in 2013 in China.By January,2018,1398 cases of avian influenza A(H7N9)laboratory-confirmed cases have been reported in mainland China,including 560 cases that have died,and the death rate of the disease is approximated by 40.06%.The disease have caused enormous damage to our economy as well as threat to people's life and safety,hence,it is of great importance and significance to study the epidemiology and the prevention of the virus theoretically.In this work,we formulate dynamic models from poultry to human to study the impacts of avail-able hospital resources,government intervention strategies,and psychological effect on the transmission of the virus.By applying qualitative analysis and numerical methods,we investigate how different strategies affect the disease evolution and seek for effective solutions to control the outbreak.Firstly,an avian influenza A(H7N9)virus transmission model with nonlinear incidence and recovery rates is constructed to understand the combined impacts of government intervention strategies(such as media,disinfection and market closure)and available hospital resources on the spread of A(H7N9)virus.The basic repro-duction number defined by the next generation matrix determines the prevalence of the virus,meanwhile,the global stability of the disease-free and endemic equilib-ria is obtained by constructing Lyapunov and Dulac functions.Numerical results reveal that government intervention strategies implemented timely and hospital resources provided adequately can effectively diminish the outbreak and postpone the peak.Secondly,because of an incubation period in human populations,an SEIR type of compartmental model is formulated to study the combined impacts of psy-chological effect and available resources of public health system on the transmission and control of A(H7N9)virus.Global stability of the disease-free and endemic e-quilibria is determined by the basic reproduction number as a threshold parameter and is obtained by constructing Lyapunov function and second additive compound matrix.Furthermore,we use partial rank correlation coefficients(PRC Cs)to find which parameter the prevalence at endemic equilibrium is sensitive to when pa-rameters vaxy.The results obtained reveal that psychological effect and available resources are the most important factors,and they can indeed diminish the final sizes of the infected.