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Related Experiment Video

Updated: Jan 3, 2026

Synthesis of Cyclic Polymers and Characterization of Their Diffusive Motion in the Melt State at the Single Molecule Level
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Analysis on a diffusive SIS epidemic system with linear source and frequency-dependent incidence function in a

Jin Zhe Suo1, Bo Li1

  • 1School of Mathematics and Statistics, Jiangsu Normal University, Xuzhou, 221116, Jiangsu Province, China.

Mathematical Biosciences and Engineering : MBE
|November 17, 2019
PubMed
Summary

This study analyzes a diffusive SIS epidemic model with a novel incidence function. The research reveals that a parameter

Keywords:
SIS model with linear sourceasymptotic profilebasic reproduction numberdisease-free equilibrium and endemic equilibriumfrequency-dependent incidence functionglobal attractivityuniform persistence

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Area of Science:

  • Epidemiology
  • Mathematical Biology
  • Dynamical Systems

Background:

  • Investigating infectious disease dynamics is crucial for public health.
  • Reaction-diffusion models are essential for understanding spatial spread of epidemics.
  • Previous models often used simpler incidence functions.

Purpose of the Study:

  • To analyze a diffusive SIS epidemic model with a frequency-dependent incidence function.
  • To explore the impact of a parameter 'c' on disease dynamics.
  • To understand the role of a linear source term in disease persistence.

Main Methods:

  • Derivation of uniform bounds for solutions.
  • Analysis of uniform persistence property.
  • Proof of global attractivity for disease-free and endemic equilibria.
  • Investigation of asymptotic profiles for small diffusion rates.

Main Results:

  • The basic reproduction number (R0) is a decreasing function of 'c'.
  • The disease can be eradicated if 'c' is sufficiently large.
  • The linear source term can promote disease persistence.
  • New dynamical behaviors emerge compared to models with c=0.

Conclusions:

  • The parameter 'c' significantly influences epidemic outcomes, offering potential control strategies.
  • The linear source term's role in enhancing persistence warrants further investigation.
  • The model provides a more nuanced understanding of infectious disease spread in heterogeneous environments.