Global Dynamics of SIRS Model with No Full Immunity on Semidirected Networks

In this paper, an epidemic model with no full immunity is analyzed on semidirected networks. Directed networks led into previous scale-free networks, and we consider that some infectious diseases do not have full immunity. So we use strong self-protection instead of immunity and establish a semidirected network infectious disease model without full immunity. The basic reproduction number R0 is calculated. If R0<1, the disease-free equilibrium E0 is locally and globally asymptotically stable. And the endemic equilibrium E∗ is globally asymptotically stable in some condition. A large number of simulation results in this paper verify the correctness of the above conclusions and provide a solution for controlling disease transmission in the future.