On a Modified Mathematical Model Arising from a Trojan Y Chromosome Strategy

Abstract

In this paper, we investigate a modified Trojan Y chromosome (TYC) strategy aimed at eradicating invasive species from natural habitats. The proposed mathematical model enhances the original TYC framework by ensuring the nonnegativity of population densities and preventing potential solution blow-up. The new model is formulated as a strongly coupled reaction–diffusion system with distinct diffusion coefficients for each species. We first establish the global well-posedness of the system. Subsequently, a stability analysis is conducted. In particular, we demonstrate that the population densities converge to zero when the birth rate for each species falls below a critical threshold. Additionally, we prove the existence of a positive steady-state solution even as the artificially introduced YY female population density tends to zero as t tends to ∞. Furthermore, we identify a bifurcation in the system’s solutions as the birth rate crosses the critical value.