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On an impulsive faecal-oral model in a periodically evolving environment

Author

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  • Zhou, Qi
  • Lin, Zhigui
  • Santos, Carlos Alberto

Abstract

To understand how impulsive intervention and regional evolution jointly influence the spread of faecal-oral diseases, this paper develops an impulsive faecal-oral model in a periodically evolving environment. The well-posedness of the model is first checked. Then, the existence of the principal eigenvalue which depends on impulse intensity and evolving rate is proved based on the celebrated Krein–Rutman theorem. With the help of this value, the threshold dynamical behaviours of the model is investigated. More importantly, this paper also derives the monotonicity of the principal eigenvalue with respect to initial region and impulse intensity, and estimates the principal eigenvalue in some special cases. Finally, numerical simulations are used to verify the correctness of the theoretical results and understand the impact of regional evolution rate on the spread of the diseases. Our research shows that large impulsive intensity 1−g′(0) and small evolving rate ρ(t) play a positive role in the prevention and control of the diseases.

Suggested Citation

  • Zhou, Qi & Lin, Zhigui & Santos, Carlos Alberto, 2025. "On an impulsive faecal-oral model in a periodically evolving environment," Chaos, Solitons & Fractals, Elsevier, vol. 191(C).
    • Handle: RePEc:eee:chsofr:v:191:y:2025:i:c:s0960077924013778
    DOI: 10.1016/j.chaos.2024.115825
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