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#Structure of the appendix:
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###### CHAPTER_3 ##########

- OCP_3.2.py: this code implements the optimal control problem (3.2) of the master thesis and reproduces Figure 3.3.

- Gradient_Descent.py: this code solves the OCP (3.2) using the gradient descent according to u

- Gradient_Descent_Log.py: this code solves the OCP (3.2) using the gradient descent according to ln(u)

- Newton_Method.py: this code solves the OCP (3.2) using the Newton's method. 

- Comparison_Methods.py: this code compares the results obtained with the different methods used to solve the OCP (3.2) (Figure 3.4).

- High_Cost_Functions.py: this codes implements the optimal control problem (3.2) of the master thesis with high cost functions for the health measures (Figure 3.6). 

- OCP_3.5.py: this code implements the optimal control problem (3.5) of the master thesis and reproduces Figure 3.7. 

###### CHAPTER_4 ##########

- MPC_4.2.py: this code implements the MPC problem (4.2) of the master thesis and reproduces Figures 4.1 and 4.2.

- Comparison_MPC_OCP.py: this code compares the results obtained in the case of the optimal control approach (Chapter 3) with the one in the case of the model predictive control approach (Chapter 4) and reproduces Figure 4.3.

###### CHAPTER_5 ##########

- MPC_Vulnerable_Pop.py: this code implements the MPC problem which considers the vulnerable sub-population and reproduces Figures 5.1 and 5.2.

###### CHAPTER_6 ##########

- MPC_Vacc.py: this codes implements the MPC problem allowing to find the optimal vaccination for the vulnerable and the non-vulnerable populations. It reproduces Figures 6.1 and 6.2.

- MPC_Vacc_Health_Professionals: this codes implements the MPC problem allowing to find the optimal vaccination for the vulnerable population, the non-vulnerable population and the health professionals. It reproduces Figure 6.3.

###### CHAPTER_7 ##########

- MPC_Epidemic_Status.py: this codes implements the MPC problem in which the measures imposed on each individual depend on their epidemic status. It reproduces Figure 7.2. 



