A structured mosquito model coupled with sterile male technique: dynamical analysis

Taking into account the stage-specific structural characteristics exhibited during mosquito development and the biological suppression of mosquito populations using the sterile male technique, this paper establishes a high-dimensional differential equations model to study the global dynamics of mosquito populations. The basic reproduction number \(\mathcal{R}_{0}\) is defined. By constructing appropriate Lyapunov functions, we prove that if \(\mathcal{R}_{0}\leq 1\) , the trivial equilibrium \(E^{0}\) is globally asymptotically stable; while if \(\mathcal{R}_{0}>1\) , the positive equilibrium Ẽ is globally asymptotically stable. Numerical simulations verify the theoretical results, and demonstrate the effectiveness of stage-structured and sterile-male-based biological control for mosquito populations.