## JCSET | Watershed Studies Institute Research Symposium

# Application of Optimal Control Theory to a Malaria Model

## Academic Level at Time of Presentation

Graduate

## Major

Mathematics

## List all Project Mentors & Advisor(s)

Dr. Maeve McCarthy; Dr. Donald Adongo; Dr. Renee Fister

## Presentation Format

Oral Presentation

## Abstract/Description

With malaria still prevalent and considered to be one of the most devastating infectious diseases in the world, many scientific efforts have been made to reduce its impact. One such effort includes the construction of mathematical models. Mathematical models can be used to analyze malaria transmission dynamics in the human population. The development of these models allows researchers to consider the control measures necessary to reduce the prevalence of malaria infection and possibly eliminate it.

The model presented in this thesis will provide the relationship of female *Anopheles* mosquitoes and insecticide treated paint acting as the control. A deterministic system of differential equations will be studied for the transmission of malaria. Optimal control theory will be used as a mathematical tool to make decisions involving this complex biological system. The desired outcome is to minimize the number of infected humans and the relative cost of paint application. The insecticide treated paint will be used as the control measure to minimize the spread of disease in a predefined time interval subject to the dynamical model and constraints for the input controls. The dynamical model is governed by a system of ordinary differential equations and will utilize Pontryagin’s Maximum Principle in the optimal control theory. Numerical simulations, such as a forward-backward sweep method will be carried out to show the effectiveness of the optimal control intervention.

## Spring Scholars Week 2021 Event

Watershed Studies Institute Symposium

Application of Optimal Control Theory to a Malaria Model

With malaria still prevalent and considered to be one of the most devastating infectious diseases in the world, many scientific efforts have been made to reduce its impact. One such effort includes the construction of mathematical models. Mathematical models can be used to analyze malaria transmission dynamics in the human population. The development of these models allows researchers to consider the control measures necessary to reduce the prevalence of malaria infection and possibly eliminate it.

The model presented in this thesis will provide the relationship of female *Anopheles* mosquitoes and insecticide treated paint acting as the control. A deterministic system of differential equations will be studied for the transmission of malaria. Optimal control theory will be used as a mathematical tool to make decisions involving this complex biological system. The desired outcome is to minimize the number of infected humans and the relative cost of paint application. The insecticide treated paint will be used as the control measure to minimize the spread of disease in a predefined time interval subject to the dynamical model and constraints for the input controls. The dynamical model is governed by a system of ordinary differential equations and will utilize Pontryagin’s Maximum Principle in the optimal control theory. Numerical simulations, such as a forward-backward sweep method will be carried out to show the effectiveness of the optimal control intervention.