Abstract

Background: An application of a novel method of a quantifier elimination for the SEIS model was presented in this paper. The appearance of the AIDS disease was crucial for developing numerous new epidemic models. We decided to analyse one of these complex models by QE method. Objective: A main aim was to investigate the existence of the Hopf bifurcation for the SEIS model. We have also analysed one complex epidemic model appropriate for AIDS disease by QE method. We applied the SEIR model in order to analyse the early phase of COVID-19 in BiH and different regions in Italy. Methods: The implementation of a new method for quantifier elimination for the theory of real closed fields (a method was implemented in Mathematica). Results: The main result was that the system which describes the SEIS model does not have a Hopf bifurcation for any parameter values for the epidemiological relevant cases. Conclusion: We applied an original implementation of QE method successfully in order to investigate the SEIS model. Considering the application of QE method to a model appropriate for AIDS disease, we were interested in change of the qualitative behaviour of a parametrized system of differential equations.

Key words: epidemic model, reproduction number, hopf bifurcation, quantifier elimination