A novel model for female population on the effects of African Stalk Borer on Saccharum officinarum L. under the sterile Insect Technology Interventions

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.