Random strategies of contact tracking

One of several critical issues in the development of optimal disease containment and eradication strategies is the knowledge of underlying contacts between individuals. Here we employ random search strategies to identify all possible links, representing direct or indirect interactions between individuals building up the system. In order to recognize all contacts, the searcher performs symmetric Lévy flights onto the accessible area. We investigate the influence of local and non-local information, the exponent characterizing asymptotic behavior of Lévy flights, boundary conditions, density of links and type of a search strategy on the efficiency of the search process. Monte Carlo examination of the suggested model reveals that the efficiency of the search process is sensitive to the type of boundary conditions. Depending on the assumed type of boundary conditions, efficiency of the search process can be a monotonic or non-monotonic function of the exponents characterizing asymptotic behavior of Lévy flights. Consequently, among the whole spectrum of exponents characterizing the power law behavior of jumps' length, there exist distinguished values of stability index representing the most efficient search processes. These exponents correspond to extreme (minimal or maximal) or intermediate values of stability index associated with Gaussian, maximally heavy-tailed or Cauchy-like strategies, respectively.