An estimative (warning) model for recognition of pandemic nature of virus infections

Abstract A simple SIS-type mathematical model of infection expansion is presented and analysed with focus on the case SARS-Cov-2. It takes into account two processes, namely, infection and recovery/decease characterised by two parameters in total: contact rate and recovery/decease rate. Its solution has a form of a quasi-logistic function for which we have introduced an infection index that, should it become negative, can also be considered as a recovery/decease index with decrease of infected down to zero. Based on the data from open sources for the SARS-Cov-2 pandemic, seasonal influenza epidemics and a pandemic in the fauna world, a threshold value of the infection index has been shown to exist above which an infection expansion pretends to be considered as pandemic. Lean (two-parameter) SIR models affined with the warning SIS model have been built. Their general solutions have been obtained, analysed and shown to be a priori structurally adjusted to the infectives’ peak in epidemiological data.