ABSTRACT In this paper some innovative aspects of the mathematical modelling of classic epidemiology problems for the study of models related to the COVID-19 pandemic dynamics are presented. In addition, they are compared to real-world data using numerical methods in order to approximate the solutions. One of these models includes a non-transmitting compartment and another one, a delay-differential equation in the SIR-type method. Finally, a comparative discussion of the results is also presented.

ABSTRACT This work addresses the COVID-19 pandemic on two fronts: proposing a system of ordinary differential equations to model it and fitting this model to Brazilian and Portuguese data. It presents estimations to important parameters for the infection dynamics, such as the percentage of asymptomatic individuals, and it stresses out that non-biological human aspects, for example, cultural, social, and economic, are not only impacted by the pandemic but also impact the pandemic dynamics itself. We state that, despite significant variations in the parameters, due to those human elements present in the contemporary pandemic, and despite the strong nonlinearities of the problem, wise human intervention is possible and able to minimize human losses. We show that the mortality rate does not behave as one would expect for a biological problem, independent of cultural aspects, and we also point to possible dates for the peaks of infection in both countries depending on the control of the transmissibility.