Bifurcation Analysis Of Two SIHR Models Affected By The Number Of Hospital Beds

Infectious disease models play an important role in the study of disease trans-mission,prevention and treatment.Based on qualitative theory and bifurcation theory of differential equations,this paper studies the bifurcation dynamics behav-ior of two SIHR models affected by the number of hospital beds.In chapter 2,we study bifurcation dynamics of SIHR model affected by the number of hospital beds.The basic reproduction number R₀is calculated using the next-generation matrix method.We analyze the existence of endemic equilibria and discuss the stability of E₀.In particular,we demonstrate the existence of backward bifurcation,saddle-node bifurcation,Hopf bifurcation,and Bogdanov-Takens bifurcation using normal form theory and central manifold theory.Numerical simulations show that the dynamic behavior of the model undergoes a transition from forward bifurcation to backward bifurcation and saddle-node bifurcation when the number of hospital beds is reduced.Our findings suggest that when the number of hospital beds C falls below the threshold C^*,backward bifurcation will occur,meaning that infection cannot be eliminated even if R₀<1.Therefore,the number of hospital beds should be increased beyond the bed threshold during an outbreak of disease,which has important implications for disease control.In chapter 3,we study the stability and Hopf bifurcation of SIHR time delay models affected by the number of hospital beds.Using the next generation matrix,we obtain the basic regenerative number R₁and the existence of disease-free equilib-rium and endemic equilibria.The disease-free equilibrium is locally asymptotically stable when R₁≤1.Taking the time delay as the bifurcation parameter,we show that Hopf bifurcation near the positive equilibrium will be produced and the sta-bility of the positive equilibrium changes whenτpasses through the critical value.Simulations of the model dynamics using the parameter values of COVID-19 show that in the case of sufficient hospital beds,when the delay is appropriately reduced,the number of infected people will decrease,indicating that increasing the number of hospital beds and timely treatment are beneficial to disease control.