In this paper, an SIR-SI epidemic model on networks is proposed to model vector-borne diseases with dual transmission modes. The basic reproduction number, \(\boldsymbol{{R_0}}\) , is calculated based on the existence of the endemic equilibrium. Subsequently, the stability of both the disease free equilibrium and the endemic equilibrium is examined. The results indicate that when \(\boldsymbol{{R_0} \leq 1}\) , the disease free equilibrium is globally asymptotically stable. Conversely, when \(\boldsymbol{{R_0} >1}\) , the endemic equilibrium is globally attractive. A sensitivity analysis is conducted to identify the key parameters, and an optimal control problem incorporating three strategies is introduced. Finally, numerical simulations are carried out to validate the theoretical conclusions and determine the optimal control strategy, providing practical insights for the prevention and control of vector-borne infectious diseases.
