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Related Experiment Videos

A diffusive SI model with Allee effect and application to FIV.

Frank M Hilker1, Michel Langlais, Sergei V Petrovskii

  • 1Institute of Environmental Systems Research, Department of Mathematics and Computer Science, University of Osnabrück, 49069 Osnabrück, Germany. fhilker@uos.de

Mathematical Biosciences
|January 3, 2006
PubMed
Summary

This study models infectious disease spread, like Feline Immunodeficiency Virus (FIV), using reaction-diffusion equations. The Allee effect significantly complicates disease dynamics, leading to extinction waves and impacting host population viability.

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Area of Science:

  • Mathematical Biology
  • Epidemiology
  • Population Dynamics

Background:

  • Infectious diseases can significantly impact host populations.
  • The Feline Immunodeficiency Virus (FIV) serves as a model for long-term infections.
  • Host population growth dynamics are crucial for understanding disease spread.

Purpose of the Study:

  • To analyze a minimal reaction-diffusion model for infectious disease spatiotemporal spread.
  • To investigate the influence of host population growth (logistic vs. Allee effect) on disease dynamics.
  • To understand the impact of Feline Immunodeficiency Virus (FIV) on cat populations.

Main Methods:

  • Development of a minimal reaction-diffusion mathematical model.
  • Inclusion of host population growth: logistic and Allee effect.

Related Experiment Videos

  • Analysis of spatiotemporal dynamics and stability of disease spread.

    • Main Results:

    • Logistic growth model shows a constant-rate travelling infection wave.
    • Allee effect model exhibits complex dynamics, including extinction waves and destabilization of endemic states.
    • Spatially restricted epidemics, extinction pulses, and recovery pulses are possible under the Allee effect.
    • The Allee effect introduces minimum viable population sizes and critical spatial scales.

    Conclusions:

    • The Allee effect dramatically alters infectious disease spread compared to logistic growth.
    • Disease-induced extinction waves can destabilize host-pathogen coexistence.
    • Transient epidemics and bistability are observed, with no sustained oscillations.