A Mathematical Model for the COVID-19 Outbreak and Its Applications

Abstract

A mathematical model based on nonlinear ordinary differential equations is proposed for quantitative description of the outbreak of the novel coronavirus pandemic. The model possesses remarkable properties, such as as full integrability. The comparison with the public data shows that exact solutions of the model (with the correctly specified parameters) lead to the results, which are in good agreement with the measured data in China and Austria. Prediction of the total number of the COVID-19 cases is discussed and examples are presented using the measured data in Austria, France, and Poland. Some generalizations of the model are suggested as well.

Keywords

• nonlinear mathematical model
• modeling infectious diseases
• logistic equation
• integrability
• exact solution