Project Overview:

The work extends the classic SIR model by integrating additional factors such as reinfection and dynamically changing death and infection rates to mimic real-world viral evolution. It employs differential equations and Python’s numerical integration tools to simulate the spread and mutation of the virus over time. Comprehensive data analysis and visualizations are used to illustrate how decreasing lethality contributes to prolonged viral persistence.

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Scope of work:

1. Model Extension and Conceptualization:
   The project builds on the traditional SIR model by adding a compartment for the deceased (D) and incorporating reinfection along with dynamic changes in death and infection rates. This approach transforms a standard epidemiological model into a tool that simulates how a virus might naturally evolve, making it understandable to a broad audience and showcasing innovative thinking that appeals to potential employers.
2. Mathematical Modeling and Differential Equations:
   At its core, the work involves solving a system of differential equations that track the evolution of four population groups—Susceptible, Infected, Recovered, and Deceased. The use of robust numerical methods, such as Python's solve_ivp() with the RK45 algorithm, highlights the technical proficiency and mathematical rigor required to accurately model disease dynamics.
3. Simulation of Viral Evolution Through Random Walks:
   The project simulates viral mutations by applying a random walk mechanism to both the infection and death rates. This method mimics natural selection, where mutations tend to favor lower lethality, and is clearly explained so that even non-specialists can appreciate how these stochastic changes drive the observed epidemiological trends.
4. Python Implementation and Data Analysis:
   Implemented in Python, the project leverages scientific libraries to solve the equations and generate simulation data. Detailed visualizations—including time series and scatter plots—provide clear insights into how changes in the parameters affect the overall dynamics, demonstrating both technical skills and the ability to communicate complex results effectively.
5. Comprehensive Visualization and Interpretation:
   Visual tools are used to depict the evolution of the infection and death rates over time, and to identify critical thresholds for viral persistence. These clear, well-labeled graphs make the findings accessible, which is essential for demonstrating the practical value of the work to prospective employers.
6. Acknowledgment of Limitations and Future Directions:
   The project openly discusses its limitations, such as the exclusion of factors like births and external contacts, and outlines potential future enhancements. This critical self-assessment shows a deep understanding of the model's constraints and a proactive approach to improving the methodology, an attractive quality for any professional setting.

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Key Takeways:

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