Mathematical Modeling and Optimal Control Strategies for Covid19 Management in India Dynamics Stability and Policy Evaluation

Abstract

Over the past two decades, infectious diseases have proliferated across the globe, underscoring newlinethe urgent need for robust mathematical models to inform public health policy decisions. The newlineswift transmission of SARS-CoV-2 and the resulting COVID-19 pandemic have highlighted newlinethe critical importance of comprehending disease transmission dynamics and implementing newlineeffective control measures. However, the predictive capacity and policy relevance of newlinetraditional epidemiological models are often limited by their inability to accommodate temporal newlineinterventions and the complexities of real-world settings. newlineThis thesis formulates and examines advanced compartmental models namely SEIR, newlineSEIHR, SIQR, and SEQIR that incorporate optimal control parameters for key public newlinehealth interventions such as immunisation, quarantine, isolation, mask usage, and awareness newlinecampaigns, thereby addressing existing model limitations. These models are subjected to newlinerigorous analysis to evaluate their influence on the basic reproduction number R0 . In newlineaddition, sensitivity analysis, local and global stability assessments, and numerical simulations newlineare conducted to substantiate the outcomes. Particular attention is given to modelling newlinescenarios pertinent to India s sociodemographic and healthcare context. Each chapter presents newlinenovel model structures with time-dependent controls designed to emulate diverse intervention newlinestrategies. Initially, the role of dynamic immunisation is explored through an enhanced SEIR newlinemodel incorporating a hospitalised compartment. Subsequently, the SIQR model is introduced newlineto reflect awareness and hygiene practices. The SEQIR model further extends the framework newlineby integrating stratified interventions such as behavioural change and isolation. Finally, a newlinemodified SEIR model is utilised to analyse the impact of non-pharmaceutical interventions, newlinewith a specific focus on mask usage newline