Background:: An application of a novel method of a quantifier elimination in epidemiology was presented in this paper Objective: We investigated the existence of the endemic equilibrium for the SEIRS model by QE method and gave a short review of the epidemic prediction models for covid-19. Methods: A new method for quantifier elimination for the theory of real closed fields. Results: Obtained value of a reproduction number and endemic equilibrium for the SEIRS model by QEAnalysis of the SEIR model with the concrete values through the example of Severe Acute Respiratory Syndrome (SARS) (a critical value of a transmission rate is evaluated in the example). Conclusion: The main result of this paper is the obtained value of the endemic equilibrium for the SEIRS model (similar result is obtained for the SEIR model). Also, we have analysed the SEIR model through the examle of SARS and we reviewed several epidemic prediction models for covid-19.
Key words: epidemic model, reproduction number, endemic equilibrium, quantifier elimination.
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