An optimal control model of mosquito reduction management in a dengue endemic region

摘要

Aedes aegypti is known as the responsible vector transmitting dengueflavivirus. Unavailability of medication to cure the transmission of the virusin the human blood becomes a global health issue in recent decades. Worldepidemiologists are encouraged to focus on the investigation over the effectiveand inexpensive way to prevent dengue transmission, i.e. mosquito control. Inthis paper, we present a model depicting the dynamics of mosquito populationbased on indoor-outdoor life cycle classification. The basic mosquito offspringnumber was obtained and analysis of equilibria was shown. We brought along adiscussion on the application of optimal control to the model in which twosimultaneous schemes were introduced. The first scheme is done by disseminatingchemical like temephos in spots where eggs and larvae develop, meanwhile thesecond scheme is done by deploying fumigation through areas where adultmosquitoes prevalently nest, indoor as well as outdoor. A version of thegradient-based method was presented to set up a workflow in minimizing theobjective functional with respect to some control variables. Numerical resultsfrom the analysis of the basic mosquito offspring number with constant controland from that with optimal control suggested that the application of fumigationis preferable over that of temephos. It was also suggested that applying bothcontrol schemes simultaneously gives the most significant reduction in thepopulation.