Related Experiment Video
Updated: Nov 22, 2025

A Method of Trigonometric Modelling of Seasonal Variation Demonstrated with Multiple Sclerosis Relapse Data
Published on: December 9, 2015
Mathematical model of SIR epidemic system (COVID-19) with fractional derivative: stability and numerical analysis
1Department of Mathematics and Statistics, College of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh, Saudi Arabia.
Abstract:
In this paper, we study and analyze the susceptible-infectious-removed (SIR) dynamics considering the effect of health system. We consider a general incidence rate function and the recovery rate as functions of the number of hospital beds. We prove the existence, uniqueness, and boundedness of the model. We investigate all possible steady-state solutions of the model and their stability. The analysis shows that the free steady state is locally stable when the basic reproduction number is less than unity and unstable when . The analysis shows that the phenomenon of backward bifurcation occurs when . Then we investigate the model using the concept of fractional differential operator. Finally, we perform numerical simulations to illustrate the theoretical analysis and study the effect of the parameters on the model for various fractional orders.
Related Concept Videos
Steps in Outbreak Investigation
Exponential Equations for Modeling Growth
Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving
In individual population analyses, different algorithms are employed, such as Cauchy's method, which uses a...
Parametric Survival Analysis: Weibull and Exponential Methods
Weibull Distribution
The Weibull distribution is a flexible model used in parametric survival analysis. It can handle both increasing and decreasing hazard rates, depending on its shape parameter...
Fundamental Mathematical Principles in Pharmacokinetics: Calculus and Graphs
On the other hand, integral calculus focuses on...
Mathematical Modeling: Problem Solving
