Mathematical modelling and analysis of Covid 19 Pandemic Dynamics and its Control

Abstract

This thesis is devoted to the mathematical understanding of the evolution and control of the newlineCOVID-19 crisis through various deterministic frameworks, aiming to better understand newlinedisease transmission, intervention strategies, and future preparedness. Initially, a compre newlinehensive review of traditional compartmental models like SIR, SIQR, SEIR, and SV IR newlineis presented, with a focus on deterministic approaches. The review synthesizes major find newlineings on intervention impacts, discusses model limitations, and highlights future directions, newlineincluding real-time data integration and hybrid modeling for enhanced pandemic prediction newlineand management. Subsequently, an adapted SIQR (Susceptible Infected Quarantine newlineRecovered) model is formulated to capture the multi-variant dynamics arising from Delta newlineand Omicron variants. The mathematical model is examined for its well-posedness and the newlineexistence of equilibrium states, and stability properties are established, followed by sensi newlinetivity and elasticity analyses to identify critical transmission parameters. To evaluate the newlineparameter sensitivity within the infection model, advanced sampling and statistical correla newlinetion methods (PRCC) are applied, highlighting the significant effects of recovery and con newlinetact tracing processes. An extended SV IR (Susceptible Vaccinated Infected Recovered) newlinemodel is also developed to study the effectiveness of vaccination strategies. The math newlineematical model is investigated with respect to its equilibrium properties and the basic newlinereproduction number R0. To explore effective intervention measures, an optimal con newlinetrol problem is designed and analyzed using the Pontryagin s Maximum Principle, which newlineprovides the necessary conditions for optimal solutions The resulting optimal vaccination newlinestrategies are validated numerically, demonstrating substantial reductions in infection rates newlineand healthcare costs compared to non-vaccination scenarios. Additionally, a comparative newlinestudy between the SEIR and SEIR-D models is conducted using real COVID-19 data newlinefrom South Korea,