Optimal epidemic intervention of HIV spread using the cross-entropy method

The spread of the human immunodeficiency virus (HIV) depends prominently on the migration of people between different regions. An important consequence of this population mobility is that HIV control strategies that are optimal in a regional sense may not be optimal in a national sense. The question is how the local governments can, individually and collectively, make better use of their budgets to reduce the number of new cases of HIV infection taking into account that people travel among regions. We formulate the problem of epidemic intervention as an optimal control problem, finding control sequences (functions) that optimize a given objective function. The mobility of people among regions is modelled via a transition graph as shown in Figure 1