Dynamics Analysis Of Vector-borne Diseases With Allee Effect And Medical Resources

Vector-borne diseases are infectious diseases in which vector transmit pathogenic microor-ganisms to animals and human hosts through biting.In recent years,global warming,habitat destruction,overfishing,environmental pollution,aging and other factors have largely affected the emergence and resurgence of vector-borne diseases in unknown ways.Infectious diseases will affect the population density.When the population density drops below a certain critical level,the population reproduction rate will decline.This phenomenon is called Allee effect,which can be seen that Allee effect affects the spread of infectious diseases.In addition,the outbreak of vector-borne diseases requires the investment of medical resources,which has a direct impact on the treatment and control of infectious diseases.Then,this paper mainly considers the influence of Allee effect and medical resources on dynamic behavior of model.In the second part of this paper,we establish and study an vector-borne disease model with Allee effect in host population,and discuss and analyze the existence and stability of the equilibria.It is find that there may be two or no disease-free equilibria and the basic reproduction numbers are obtained.It is further prove that the disease-free equilibrium with a small number of susceptible population is the saddle,and the disease-free equilibrium with a large number of susceptible pop-ulation is a node point.When the two disease-free equilibria coincide,which is the saddle node.By further analysis,we find that the system may have zero,one,two or three positive equilibria,the conditions of local asymptotically stability for positive equilibria and the occurrence for Hopf bifurcation are given by Routh-Hurwitz criterion.Through numerical simulation,the existence of the number of positive equilibria is verified,and it is find that the model undergoes saddle-node,Bogdanov-Takens and Hopf bifurcation.Since the availability of medical resources is the main factor affecting the recovery rate,in the third part of this paper,we consider the model of vector-borne disease with nonlinear recovery rate of host population and study the dynamic behavior of the model.Firstly,the basic reproduction number and disease-free equilibrium of the system are given.By analysis,it is shown that the disease-free equilibrium is locally asymptotically stable when₀<1.When₀>1,the disease-free equilibrium is unstable.In the system,there may exist two,one or no positive equilibria.If there are two positive equilibria,one of the small number of infected population is a saddle type.The other one is stable or unstable.Thus,the system undergoes Hopf bifurcation.By numerical simulation we find that system undergoes saddle-node,Hopf and Bogdanov-Takens bifurcation.Furthermore,we verify that the system has a stable limit cycle.The results will provide a theoretical basis for controlling the spread of vector-borne diseases.