Developing and investigating mathematical models for simulation and control of some infectious diseases.

Abstract

This thesis constructs and analyzes mathematical models to simulate and control specific infectious diseases, with a primary emphasis on tuberculosis (TB). Both continuous and discrete dynamical systems are utilized to study disease spread and evaluate the effectiveness of public health measures. Some compartmental models are formulated to represent different stages of infection, key risk factors, and control measures such as vaccination, chemoprophylaxis, and public health policies. Real-world data from Algeria, Ukraine, India, and Russia are used to evaluate the effectiveness of these strategies in various demographic and healthcare contexts. In addition, game theory is applied to study vaccination behavior, using Nash equilibrium concepts to account for factors such as perceived risk, cost, and disease prevalence. By integrating mathematical modeling with strategic decision-making approaches, this study enhances disease control strategies and promotes better public health outcomes.