ON MODIFIED VARIANTS OF CLASSICAL TROJAN Y CHROMOSOME MODEL WITH GLOBAL SOLUTIONS

Abstract

The Trojan Y Chromosome (TYC) strategy is a biological control method for controlling invasive populations with an XX–XY sex determinism, wherein a modified organism is introduced into an invasive population to skew the sex ratio over time, causing local extinction. However, the classical three compartment TYC model possesses blow-up solutions, for large initial conditions [Takyi EM, Beauregard MA, Griffin T, Bobo L, Parshad RD, On large and small data blow-up solutions in the Trojan Y Chromosome model, Axioms 11(3):120, 2022]. We investigate model improvements via accounting for a modified logistic term, female mating preference, competition between males and supermales and pair formation. Each one of these models is dynamically explored and is shown to possess global in-time non-negative solutions, in any parameter and initial data regime, and the models are also effective in facilitating extinction of the invasive wild type.