Study on Dynamical Behavior of Coinfection Infectious Disease Model (2503.09472v1)

Abstract: This paper conducts research on the established model and presents the main conclusions . Firstly, by separately considering the infectivity of each of the two infectious diseases and the infectivity of the population simultaneously infected with the two infectious diseases, the existence of three types of boundary equilibrium points is determined, as well as the existence of the interior equilibrium point when the parameters are under specific conditions. Then, the stability of the equilibrium points is analyzed. It is concluded that under different parameter conditions, the stability of the disease free equilibrium point can exhibit various scenarios, such as a stable node or a saddle-node, etc. For the boundary equilibrium points, the situation is more intricate,and a cusp may occur. The stability of the interior equilibrium point under specific conditions is also presented. Finally,the degeneracy of the equilibrium points is studied through the bifurcation theory.Mainly, the saddle-node bifurcation occurring at the interior equilibrium point is obtained, and when the infection rate of the first infectious disease, the infection rate of the second infectious disease, and the infection rate of the co-infected population to other populations are selected as bifurcation parameters, a codimension 3 B-T bifurcation is obtained.