Mathematical Modeling of Infectious Diseases Using Network Theory and Stochastic Processes

1. Introduction 1.1 Background and Motivation 1.2 Objectives of the Research 1.3 Structure of the Thesis 2. Mathematical Foundations 2.1 Basic Concepts of Network Theory 2.2 Overview of Stochastic Processes 2.3 Mathematical Tools for Modeling 3. Network Theory in Disease Modeling 3.1 Types of Networks in Epidemiology 3.2 Network Properties and Disease Dynamics 3.3 Examples of Network-Based Models 4. Stochastic Processes in Epidemiology 4.1 Introduction to Randomness in Modeling 4.2 Stochastic Differential Equations 4.3 Applications in Infectious Disease Modeling 5. Combined Approach: Network Theory and Stochastic Processes 5.1 Integrating Networks with Randomness 5.2 Advantages Over Traditional Methods 5.3 Case Studies 6. Model Implementation and Simulation 6.1 Choosing Appropriate Models 6.2 Computational Tools and Techniques 6.3 Analysis of Simulation Results 7. Challenges and Limitations 7.1 Data Availability and Quality 7.2 Computational Complexity 7.3 Interpretability of Results 8. Conclusions and Future Research 8.1 Summary of Findings 8.2 Implications for Public Health Policy 8.3 Directions for Further Studies