Related Experiment Video
Updated: Oct 31, 2025

A Method of Trigonometric Modelling of Seasonal Variation Demonstrated with Multiple Sclerosis Relapse Data
Published on: December 9, 2015
Mathematical modeling and dynamic analysis of SIQR model with delay for pandemic COVID-19
Hongfan Lu1, Yuting Ding1, Silin Gong1
1Department of Mathematics, Northeast Forestry University, Harbin, 150040, China.
Abstract:
On the basis of the SIQR epidemic model, we consider the impact of treatment time on the epidemic situation, and we present a differential equation model with time-delay according to the characteristics of COVID-19. Firstly, we analyze the existence and stability of the equilibria in the modified COVID-19 epidemic model. Secondly, we analyze the existence of Hopf bifurcation, and derive the normal form of Hopf bifurcation by using the multiple time scales method. Then, we determine the direction of Hopf bifurcation and the stability of bifurcating periodic solutions. Finally, we carry out numerical simulations to verify the correctness of theoretical analysis with actual parameters, and show conclusions associated with the critical treatment time and the effect on epidemic for treatment time.
Related Concept Videos
Mathematical Modeling: Problem Solving
Exponential Equations for Modeling Growth
Steps in Outbreak Investigation
Linear time-invariant Systems
The input-output behavior of an LTI system can be fully defined by its response to an impulsive excitation at its input. Once this impulse response is known, the system's reaction to any other input can be...
Quadratic Models
Relation between Mathematical Equations and Block Diagrams

