Abstract:
Sugarcane is an important plant, not only for its economic value but its ecological importance. An infestation of E.
Walker Lepidoptera pyralidae, which occurs naturally in wetland habitats and tall grasses, ravages the sugarcane stalk
reducing its value. The study proposes a novel model for formulating the dynamics of the E. walker population with
SIT. A mathematical analysis of the proposed governing equations representing the model has unique and positive
solutions. A basic reproduction number computed based n wild free equilibrium (WFE) points was found to be R0 < 1
indicating an eminent wipeout of the wild E. walker population under SIT. The local stability of the WFE indicated
that the established R0 was locally asymptotically stable and R0 < 1. The global stability showed that WFE is globally
asymptotically stable when R0 < 1. The numerical simulation revealed that the wild E. walker population under
Sterile Insect Technology (SIT) will be wiped out after more than 120 weeks, which is unrealistic, considering that the
sugarcane matures after approximately 78 weeks. Elasticity analysis of the model parameters based on R0 indicated
that a possible control lies in controlling the eggs laid and sex ratio. The effectiveness of the control is indicated in
the numerical simulation that showed that the population of the wild E. walker is wiped out after approximately 130
weeks. Future studies into the area need to refocus on the timelines to investigate other strategies to reduce the wild
E. walker population below the sugarcane maturity stage.
