Discrete-time models for interactive wild and sterile mosquitoes with general time steps

Different from the discrete-time population models based on evolution of generations or life cycles, we formulate discrete-time homogeneous and stage-structured models with time steps in more general settings such that survivals are included at each time step. We assume that sterile mosquitoes are released and their number in the field is kept at a constant level. We study the interactive dynamics of wild and sterile mosquitoes where only sexually active sterile mosquitoes are considered. We determine threshold values of releases and investigate the interactive dynamics for both homogeneous and stage-structured populations. Numerical examples are provided to confirm and demonstrate the obtained theoretical results.