The Influence of the Asymptomatic Transmission on the Number Symptomatic Cases Within a Modified SIR Model

We consider an extension of the classical SIR model in epidemiology which considers two type of infectious states: symptomatic and asymptomatic. By using a Monte Carlo optimization method based on the simulated annealing algorithm we perform a parameter identification in order to match statistical data related to the COVID-19 pandemics in Germany between mid-2020 and beginning of 2021. Since in this period the population was not vaccinated, additional effects due to this feature can be excluded. Our analysis also takes into account the facts that for a part of the available data the symptomatic/asymptomatic status is unknown and that within the parameter set of the optimization problem we have to introduce corresponding detecting probabilities, since not all existing cases were also recorded. The results turn out to provide insights related to the transmission mechanism related to the symptomatic/asymptomatic groups, as well as to their detection probabilities.