A mathematical model for the efficient control of the New World screwworm

Abstract

An outbreak of New World screwworm has recently been spreading across Mexico, after more than 30 years of absence. The sterile insect technique, which consists of the massive release of sterilized males, has proven to be one of the most efficient methods for controlling the screwworm pest. However, given the limited number of sterile males available, improving the release strategy is critical. We propose a mathematical model of population dynamics adapted to the biology of Cochliomyia hominivorax and derive a feedback control function to determine the number of sterile males to release. We further construct a Luenberger observer to estimate wild fly populations from infected animal counts--the variable monitored by Mexican sanitary authorities--enabling field implementation of the control function. We show that eradication is achievable within approximately 60-100 weeks and that eradication time is governed primarily by the intrinsic biology of the system rather than by infestation magnitude. We then extend the model to a spatially explicit framework and show that when sterile male releases are applied at the outbreak focus and within a 120 km radius, eradication of the pest is attainable.