Analysis and complexity of pandemics

Realistic epidemic models assume network propagation in a stochastic fashion, where the disease is disseminated through neighboring nodes. Here, we study node-immunization techniques, where the notion of immunization means node-deletion in a graph. In a highly virulent scenario, a pandemic takes effect, and the disease is spread all over the connected component of a graph. A combinatorial optimization problem is introduced, where the goal is to choose a node-immunization strategy to reduce the expected number of deaths in pandemics. We prove that this problem belongs to the NP-Complete class. As corollary, a large family of node-immunization problems arising from epidemic modelling are computationally hard as well. The value of the paper is to confirm the intuition behind the fact that it is hard to cope with epidemics. The paper is closed with heuristics in order to address the combinatorial problem for pandemic analysis.