Related Experiment Video
Updated: May 5, 2026

A Method of Trigonometric Modelling of Seasonal Variation Demonstrated with Multiple Sclerosis Relapse Data
Published on: December 9, 2015
Positive periodic solutions of an epidemic model with seasonality
Gui-Quan Sun1, Zhenguo Bai, Zi-Ke Zhang
1Complex Sciences Center, Shanxi University, Taiyuan 030006, China ; School of Mathematical Sciences, Shanxi University, Taiyuan, Shanxi 030006, China ; Department of Mathematics, North University of China, Taiyuan, Shanxi 030051, China.
Abstract:
An SEI autonomous model with logistic growth rate and its corresponding nonautonomous model are investigated. For the autonomous case, we give the attractive regions of equilibria and perform some numerical simulations. Basic demographic reproduction number R d is obtained. Moreover, only the basic reproduction number R 0 cannot ensure the existence of the positive equilibrium, which needs additional condition R d > R 1. For the nonautonomous case, by introducing the basic reproduction number defined by the spectral radius, we study the uniform persistence and extinction of the disease. The results show that for the periodic system the basic reproduction number is more accurate than the average reproduction number.
More Related Videos
12:21A Mouse Model for the Transition of Streptococcus pneumoniae from Colonizer to Pathogen upon Viral Co-Infection Recapitulates Age-Exacerbated Illness
Published on: September 28, 2022
10:11Modeling The Lifecycle Of Ebola Virus Under Biosafety Level 2 Conditions With Virus-like Particles Containing Tetracistronic Minigenomes
Published on: September 27, 2014
Related Concept Videos
Infectious Diseases and Their Occurrence
Steps in Outbreak Investigation
Modeling with Differential Equations
Exponential Equations for Modeling Growth
Exponential Equations with Logarithms: Problem Solving
Population Growth