Monte Carlo simulation of COVID-19 pandemic using Planck’s probability distribution

Abstract

We present a Monte Carlo simulation model of an epidemic spread inspired on physics variables such as temperature, cross section and interaction range, which considers the Plank distribution of photons in the black body radiation to describe the mobility of individuals. The model consists of a lattice of cells that can be in four different states: susceptible, infected, recovered or death. An infected cell can transmit the disease to any other susceptible cell within some random range 𝑅. The transmission mechanism follows the physics laws for the interaction between a particle and a target. Each infected particle affects the interaction region a number 𝑛 of times, according to its energy. The number of interactions is proportional to the interaction cross section 𝜎 and to the target surface density 𝜌. The discrete energy follows a Planck distribution law, which depends on the temperature 𝑇 of the system. For any interaction, infection, recovery and death probabilities are applied. We investigate the results of viral transmission for different sets of parameters and compare them with available COVID-19 data. The parameters of the model can be made time dependent in order to consider, for instance, the effects of lockdown in the middle of the pandemic.