Abstract
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.
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