A Randomized Complexity-theoretic Model of Bio-inspired Mobile Epidemics via Close Contact

In this paper we present a randomized complexity theoretic model for those epidemics propagated via short-distance close contact. We prove that the contact-based epidemics problems fall into the Randomized Polynomial (RP) complexity class. We draw an analogy between our complexity-theoretic model and the complexity-theoretic foundation of modern cryptology. Both of them are built on top of the concept of “negligible”. In the crypto model, the failure probability of a provably secure system is negligible given the input metric n, which is the crypto key length. In our model, the failure probability of the infectious sources is negligible given the input metric ρ, which is the network density (the number of network nodes per unit area). In addition, this negligibility guarantee is an asymptotic invariant in the entire system.