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Dynamics by control strategies targeting the effective reproduction number

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  • Bartha, Ferenc A.
  • Röst, Gergely

Abstract

We construct a control system for an epidemics, where the aim of the control is to keep the effective reproduction number below a tolerance level. We assume an on–off type non-pharmaceutical intervention, which is triggered whenever the effective reproduction number goes beyond a threshold value, and its implementation occurs with some fixed time delay. The resulting hybrid system includes discontinuities, and can be formulated as an algebraic-delay-differential system. A mathematical challenge is that the past of the control is contributing to the past effective reproduction number the current control is based on. To overcome this obstacle, we define an extended phase space, and explore the dynamics of the system for various parameter domains and control strategies. We show some convergence results as well as point out the possibility of sustained oscillations under this control scheme.

Suggested Citation

  • Bartha, Ferenc A. & Röst, Gergely, 2025. "Dynamics by control strategies targeting the effective reproduction number," Chaos, Solitons & Fractals, Elsevier, vol. 191(C).
    • Handle: RePEc:eee:chsofr:v:191:y:2025:i:c:s0960077924014589
    DOI: 10.1016/j.chaos.2024.115906
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