Dynamics of two-strain epidemic model with imperfect vaccination on complex networks

Vaccination is widely recognized as a powerful tool in controlling the spread of diseases. However, it is important to acknowledge that some diseases are not completely preventable by vaccines, meaning that the protective effect of certain vaccines is not absolute. Additionally, the effectiveness of vaccines may diminish over time, which implies that even with completed vaccinations, there remains a potential risk of infection. Therefore, conducting comprehensive studies on how these imperfect vaccines impact the dynamics of disease transmission is crucial. In this study, we formulate and analyze a two-strain epidemic model with imperfect vaccination on complex networks. We derive the basic reproduction number and introduce the invasion reproduction numbers corresponding to each strain. Using the Lyapunov function method and LaSalle’s invariance principle, we demonstrate the global asymptotical stability of the disease-free equilibrium and dominant equilibrium. Furthermore, we apply persistence theory to verify the existence of coexistence equilibrium and the persistence of the disease. To validate our theoretical findings, we conduct numerical simulations. Through these simulations, we confirm that vaccination plays a significant role in controlling the spread of diseases, despite the imperfect efficacy of certain vaccines in specific cases. These findings highlight the importance of continued efforts to improve vaccine effectiveness and explore alternative strategies to enhance disease control measures.