Mathematical Modelling and Optimal Control for Infectious Diseases: Covid-19 Application

Abstract

A clear understanding of the interplay between human behavior and infectious disease dynamics is essential for designing effective intervention and mitigation strategies. In this thesis, we explore and analyze modified versions of the basic Kermack–McKendrick model that incorporate behavioral dynamics into disease transmission. Unlike traditional epidemic models, our approach accounts for how adaptive levels of caution within the population and their attitudes toward perceived safety influence the nonlinear transmission rate. This provides a more realistic framework for assessing the impact of interventions such as vaccination and education.
We established the well-posedness of each model and derive conditions for both local and global stability of the equilibria using Lyapunov function, LaSalle’s Invariance Principle, and other well-established stability criteria. To design effective mitigation strategies, we formulated optimal control problems, considering vaccination alone and vaccination combined with education campaigns. By applying Fleming and Rishel’s theorem and Pontryagin’s Maximum Principle, we determine the optimal vaccination and education policies that minimize infection levels while balancing implementation costs.
Numerical simulations validated our theoretical findings, demonstrating that integrated vaccination and educational awareness strategies can significantly reduce both disease prevalence and financial burdens. Our results highlight the importance of behavioral responses in epidemic control and provide actionable insights for policymakers seeking to design cost-effective, adaptive intervention strategies.

Date of Award	2025
Original language	American English
Supervisor	Mo'Tassem Al Arydah (Supervisor)