Global stability analysis of two strains epidemic model with imperfect vaccination and immunity waning in a complex network

For some epidemic diseases, there exist several strains of the pathogen, which can pose a challenge in controlling the disease and result in complicated dynamics, such as dengue fever and HIV. However, we lack the deep understanding of the dynamic features of interacting multiple strains. In order to reduce the final size of infections and achieve the herd immunity, vaccination is the most effective way of controlling an outbreak. To this end, we put forward the two-strain epidemic model in which vaccination is not perfect and immunity wanes in a complex network. It can be revealed that the disease free equilibrium point of two strains is global asymptotically stable when max{R-1, R-1} < 1, but the coexistence equilibrium point remains and is stable when min{R-1, R-1} > 1. Then, to verify the global stability of each strain dominance equilibrium point, the critical values are further derived. Finally, numerical simulations have been performed to visualize the results of the theoretical analysis. The current results are beneficial to comprehending the dynamics behaviors of multi-strain epidemics.