PhD Comprehensive Exam | Hassaan Qazi, Applications of Control Methods to Life Sciences

DC 1304

Candidate

Hassaan Qazi | Applied Mathematics, University of Waterloo

Title

Applications of Control Methods to Life Sciences

Abstract

We intend to present solutions to two research problems in our dissertation. The first problem is the mitigation of mosquito-borne diseases in which we would like to demonstrate some meaningful numerical results using an impulsive optimal control scheme for the release of sterile mosquitoes. Diseases that are caused by mosquito bites are a menace to humans worldwide as they cause lethal infections such as Dengue and Malaria. Since no vaccines are available, therefore it is imperative to control the population of mosquitoes. One of the strategies revolving around mosquito population reduction is a heavy use of insecticides. This method can have harmful impacts on the environment and may make mosquitoes resistant to these chemicals with time. The other strategy is to release genetically modified male mosquitoes in the wild so that they can mate with their female counterparts and make them infertile. One challenging task is to find a neat trade-off between the number of sterile mosquitoes released and the cost attached to it. Impulsive control strategy seems to move in that direction where we adopt a cost functional that takes both the cost and the effectiveness of the release of sterile insects into account. In this study, we extend the work presented by (Huang et. al., 2021) by modifying the model to have separate compartments for wild male and wild female mosquitoes. To find a cost-effective release strategy, we will compare two cost functionals; one comprising of only economic cost and the other containing both economic cost and the cost of wild population in the environment.

In our second project, a swarm of Unmanned Aerial Vehicles (UAVs) will be deployed for environmental and infrastructure monitoring with applications in, but not limited to, agriculture and aeronautics. This will be achieved by transporting the distribution of the multi-agent system towards the desired density distribution. The multi-agent system will be equipped with different sensors to take the required measurements over a field of interest at varying positions and times. The control strategy will be comprised of both centralized and distributed hierarchies. The goal is to formulate a suitable link between these two levels of the controller while taking the effects induced by the discretization of the mathematical framework into account. There has been a growing interest in the study of mean-field feedback control that can make the swarm density converge to the desired distribution but optimal control strategies for the cases when the agents’ states include stochastic behaviour and when the target density is time-varying have been limited. We would like to design an optimal feedback control along with finding the necessary optimality conditions while incorporating energy and other real-life constraints.