  Effective containment of spreading processes such as epidemics requires
accurate knowledge of several key parameters that govern their dynamics. In
this work, we first show that the problem of identifying the underlying
parameters of epidemiological spreading processes is often ill-conditioned and
lacks the persistence of excitation required for the convergence of adaptive
learning schemes. To tackle this challenge, we leverage a relaxed property
called initial excitation combined with a recursive least squares algorithm to
design an online adaptive identifier to learn the parameters of the
susceptible-infected-susceptible (SIS) epidemic model from the knowledge of its
states. We prove that the iterates generated by the proposed algorithm minimize
an auxiliary weighted least squares cost function. We illustrate the
convergence of the error of the estimated epidemic parameters via several
numerical case studies and compare it with results obtained using conventional
approaches.
