In the past decade an increased interest has been exhibited in spatiotemporal epidemic spread from the scope of stochastic approaches. To this end, the most commonly employed algorithms are variations of the Monte Carlo (MC) random sampling method. For systems out-of-equilibrium in particular, the Kinetic MC (KMC) algorithm gives a much more accurate picture than the traditional MC one.
In our case, we shall study a Susceptible-Infected-Recovered-Susceptible (SIRS) kinetic transitional model using traditional MC algorithms as well as the KMC variation. The kinetic scheme is as follows:
S+I-->I+I through a transitional rate k1 (we assume that an I site is in the first neighbour proximity of an Site)
I-->R through a transitional rate k2
R-->S through a transitional rate k3
We shall assume both parallel (traditional MC code) and sequential updates (KMC code) of the system for each MC step. In addition, we include mobility dynamics (diffusion) for each site of the distributed population.
A serial code has been developed with sequential updating of the system on a 1D chain and 2D square lattice (grid), much in the fashion of the respective Ising models.
With the expertise of our host in Florence (Politi-Torcini), our collaborators from the physics department in Bologna (Turchetti et al.) and the HPC group of CINECA we aim to optimise the existing serial code for the KMC case and to develop a highly efficient one for an implementation with parallel updating of the system (traditional MC sampling method).
Finally, a crucial goal will be to speed up our large scale runs of the KMC case via parallelisation of the code for both cases of the system update. Currently, a single (serial) run on a square grid of 103x103 lattice points (individuals) and for 100 MC steps exceeds 23 hours, a score which we expect to reduce vastly with the use of the CINECA resources. The final results should be temporal evolutions of the different species of the system for different realisations (parameter values).
To begin with, the collaboration with our host and department of physics in Bologna was successful in the development of the serial code for the case of the parallel update of the system, and therefore a comparison with the respective sequential update case was realised. As suspected, the two methods led to different results (specifically different steady states for the same parameter values), but surprisingly the sequential update case reached a noisy steady state instead of a constantly evolving (at least oscillatory if not chaotic) as was expected. This is something to be further investigated in future work. For debugging purposes, the gdb package was employed from the GNU suite of the PLX cluster in CINECA.
Furthermore, extensive discussions and prospects on statistical data analysis as well as theoretical derivations from these results were exchanged with our host in Florence and our collaborators at the department of physics in Bologna which will certainly be studied in work to follow.
As far as parallelisation is concerned, a lengthy search in the literature and discussions with Andrew Emerson of the HPC group of CINECA took place in order to decide which would be the best implementation of parallelisation on the SIRS simulations under study. The conclusion was that a modified Game of Life (Conway 1970) code would be the best for the SIRS simulations, both for the sequential and parallel updating of the system. A lot of time has been spent on debugging and profiling (for scalability) the code using the DDT debugging package and the gprof profiler available from the PLX cluster in CINECA.
Due to no prior experience in parallel programming at the beginning of the visit in CINECA and due to extensive search and theoretical work before venturing into the parallel implementation, the codes are in a final form but in the process of debugging and trial runs. Within the end of the following month we expect to have a working code scaled to finalise within the span of an hour, thus fulfilling our initial expectations. This short term work shall continue via remote access of the PLX cluster of CINECA from our home institute in Athens.