In this paper, we present LOIMOS, which is an epidemiological scenario simulator developed in the context of the fight against the pandemic caused by coronavirus SARS-CoV-2 on a global scale. LOIMOS has been fully developed under the paradigm of membrane computing using transition P systems with communication rules, active membranes and a stochastic simulator engine. In this paper we detail the main components of the system and we report some examples of epidemiological scenarios evaluated with LOIMOS.

Catalytic P systems are among the first variants of membrane systems ever considered in this area. This variant of systems also features some prominent computational complexity questions, and in particular the problem of using only one catalyst in the whole system: is one catalyst enough to allow for generating all recursively enumerable sets of multisets? Several additional ingredients have been shown to be sufficient for obtaining computational completeness even with only one catalyst. In this paper, we show that one catalyst is sufficient for obtaining computational completeness if either catalytic rules have weak priority over non-catalytic rules or else instead of the standard maximally parallel derivation mode, we use the derivation mode maxobjects, i.e., we only take those multisets of rules which affect the maximal number of objects in the underlying configuration.

We propose a new variant of tissue P systems, with oriented division rules and external inputs. The oriented division rules are based on Hilbert’s space filling curve, more precisely on a new variant of parallel array rewriting rules, which generate Hilbert words of different ’resolutions’ in array representation. The P systems introduced here have also the capability to receive input from an external source. This is illustrated with a simple problem, that of approximating the contour of a 2D picture.

Many variants of P systems with active membranes are able to solve traditionally intractable problems. Sometimes they also characterize well known complexity classes, depending upon the computational features they use. In this paper we continue the investigation of the importance of (minimal) cooperative rules to increase the computational power of P systems. In particular, we prove that monodirectional shallow chargeless P systems with active membranes and minimal cooperation working in polynomial time precisely characterise $$\mathbf{P }^{\#{\mathbf{P }}}_{\parallel }$$ , the complexity class of problems solved in polynomial time by deterministic Turing machines with a polynomial number of parallel queries to an oracle for a counting problem.

There have been a few NP-hard problems solved using cP systems including the travelling salesman problem. However, these problems are typically in NP rather than higher in the polynomial time hierarchy. In this paper, we solve QSAT (also known as TQBF), which is a well-known PSPACE-complete problem. Compared to other extant confluent P systems solutions, our deterministic cP solution only uses a small constant number of custom alphabet symbols (19), a small constant number of rules (10) and a small constant upper limit of membrane nesting depth (6), independent of the problem size.