Pandæsim: An Epidemic Spreading Stochastic Simulator

SIMPLE SUMMARY: In order to study the efficiency of countermeasures used against the Covid-19 pandemic at the scale of a country, we designed a model and developed an efficient simulation program based on a well known discrete stochastic simulation framework along with a standard, coarse grain, spatial localisation extension. Our particular approach allows us also to implement deterministic continuous resolutions of the same model. We applied it to the Covid-19 epidemic in France where lockdown countermeasures were used. With the stochastic discrete method, we found good correlations between the simulation results and the statistics gathered from hospitals. In contrast, the deterministic continuous approach lead to very different results. We proposed an explanation based on the fact that the effects of discretisation are high for small values, but low for large values. When we add stochasticity, it can explain the differences in behaviour of those two approaches. This system is one more tool to study different countermeasures to epidemics, from lockdowns to social distancing, and also the effects of mass vaccination. It could be improved by including the possibility of individual reinfection. ABSTRACT: Many methods have been used to model epidemic spreading. They include ordinary differential equation systems for globally homogeneous environments and partial differential equation systems to take into account spatial localisation and inhomogeneity. Stochastic differential equations systems have been used to model the inherent stochasticity of epidemic spreading processes. In our case study, we wanted to model the numbers of individuals in different states of the disease, and their locations in the country. Among the many existing methods we used our own variant of the well known Gillespie stochastic algorithm, along with the sub-volumes method to take into account the spatial localisation. Our algorithm allows us to easily switch from stochastic discrete simulation to continuous deterministic resolution using mean values. We applied our approaches on the study of the Covid-19 epidemic in France. The stochastic discrete version of Pandæsim showed very good correlations between the simulation results and the statistics gathered from hospitals, both on day by day and on global numbers, including the effects of the lockdown. Moreover, we have highlighted interesting differences in behaviour between the continuous and discrete methods that may arise in some particular conditions.