When introducing the SIR model, in our initial post, we got an ordinary differential equation, but we did not really discuss stability, and periodicity. It has to do with the Jacobian matrix of the system. But first of all, we had three equations for three function, but actuallyso it means that our problem is here simply in dimension 2. Henceand therefore, the Jacobian of the system isWe should evaluate the Jacobian at the equilibrium, i.e. andWe should then look at eigenvalues of the matrix. … Continue reading …