Bifurcation analysis of a SEIR epidemic system with governmental action and individual reaction

• Published in: Advances in difference equations Vol. 2020; no. 1; pp. 541 - 14
• Main Authors: Ajbar, Abdelhamid, Alqahtani, Rubayyi T.
• Format: Journal Article
• Language: English
• Published: Cham Springer International Publishing 01.10.2020; Springer Nature B.V; SpringerOpen
• Subjects: Analysis; Bifurcation; COVID-19; Difference and Functional Equations; Epidemics; Exponential functions; Functional Analysis; Governmental action; Hopf bifurcation; Individual response; Mathematical models; Mathematical Models of Infectious Diseases; Mathematics; Mathematics and Statistics; Ordinary Differential Equations; Parameters; Partial Differential Equations; SEIR model; Stability; Stable oscillations; Step functions; Bifurcation; SEIR model; Stability; Hopf bifurcation; Individual response; Governmental action
• ISSN: 1687-1847; 1687-1839; 1687-1847
• DOI: 10.1186/s13662-020-02997-z

In this paper, the dynamical behavior of a SEIR epidemic system that takes into account governmental action and individual reaction is investigated. The transmission rate takes into account the impact of governmental action modeled as a step function while the decreasing contacts among individuals responding to the severity of the pandemic is modeled as a decreasing exponential function. We show that the proposed model is capable of predicting Hopf bifurcation points for a wide range of physically realistic parameters for the COVID-19 disease. In this regard, the model predicts periodic behavior that emanates from one Hopf point. The model also predicts stable oscillations connecting two Hopf points. The effect of the different model parameters on the existence of such periodic behavior is numerically investigated. Useful diagrams are constructed that delineate the range of periodic behavior predicted by the model.