  We study the problem of estimating the parameters (i.e., infection rate and
recovery rate) governing the spread of epidemics in networks. Such parameters
are typically estimated by measuring various characteristics (such as the
number of infected and recovered individuals) of the infected populations over
time. However, these measurements also incur certain costs, depending on the
population being tested and the times at which the tests are administered. We
thus formulate the epidemic parameter estimation problem as an optimization
problem, where the goal is to either minimize the total cost spent on
collecting measurements, or to optimize the parameter estimates while remaining
within a measurement budget. We show that these problems are NP-hard to solve
in general, and then propose approximation algorithms with performance
guarantees. We validate our algorithms using numerical examples.
