SIR final size that we can use to demonstrate the fate of S

This code utilises optimisation twice, for parametric approximation and for disease fate by optimising S_{\infty}. I hope it will help!

STAGE 1

We use optimization techniques to fit the parameters α and β by

minimizing the error function:

min

α,β

nX

i=1

(yactual,i − ypredicted,i (α, β))2

▶ Various optimization algorithms can be used, such as gradient

descent or least squares.

▶ MATLAB functions like fminsearch or lsqcurvefit are

commonly used.

STAGE 2

We present graphical results from the SIR model with fitted

parameters:

▶ Infected Data and Model Predictions:

▶ The plot shows actual infection data alongside predictions

generated by the SIR model.

▶ The model was used to estimate susceptible populations S(t)

based on given infected data.

▶ Susceptible Population (S(t)):

▶ The plot of S(t) was derived from the model, given the

constraints and conditions applied.

▶ The green star represents the optimized final size S∞, obtained

through constrained optimization.

▶ Note that S∞ is shown within the context of the model’s

predictions and the given infected data.