A Study Of Infectious Disease Models And Their Branch Problems Considering The Effect Of The Number Of Hospital Beds

In order to describe the effect of the number of hospital beds on the spread of infectious diseases,we express the hospitalized rate as a nonlinear function related to the number of empty beds and establish a SIHR infectious disease model including the hospitalized population.Then the model is analyzed theoretically and numerically.The existence and stability of the equilibria are analyzed.Moreover,we prove that the model undergoes backward bifurcation,Hopf bifurcation and Bogdanov-Takens bifurcation of codimension 2 by the center manifold and normal form methods.Our results show that there is a threshold for the number of hospital beds in a region.If the number of beds is lower than this threshold,the backward bifurcation will occur,which means that controlling the basic reproduction number to a level less than 1 is not sufficient to ensure that the disease does not break out.One should compare the actual number of beds with the threshold to avoid misjudgment and try to increase the number of beds above this threshold before adopting disease control measures.Increasing the number of hospital beds can help people ensure the ultimate extinction of the disease when the basic reproduction number is less than 1.It can also effectively reduce the number of infections and help control the spread of the disease.The estimation method of thresholds can also help people rationally allocate the number of hospital beds in a region.