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Viable control of an epidemiological model.

Michel De Lara1, Lilian Sofia Sepulveda Salcedo2

  • 1Université Paris-Est, Cermics (ENPC), F-77455 Marne-la-Vallée, France.

Mathematical Biosciences
|July 31, 2016
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This study explores limiting peak human infections during epidemics using vector mortality control. It defines viable states and introduces the concept of a viability kernel to manage infection spread.

Keywords:
Control theoryDengueEpidemiologyRoss-Macdonald modelViability theory

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Area of Science:

  • Mathematical Epidemiology
  • Disease Dynamics Modeling

Background:

  • Epidemic control typically aims for zero infections, but transient peaks can be high.
  • Controlling peak infection levels is a critical challenge in public health.

Purpose of the Study:

  • To investigate methods for limiting peak human infections during epidemics.
  • To analyze a controlled Ross-Macdonald model with vector mortality as a control variable.

Main Methods:

  • Utilized a controlled Ross-Macdonald epidemiological model.
  • Defined and analyzed the 'viability kernel' as the set of viable states.
  • Investigated three scenarios based on control capacity and infection caps.

Main Results:

  • Characterized the viability kernel into three cases: comfortable, desperate, and viable.
  • Demonstrated that viability depends on control capacity and infection thresholds.
  • Applied the model to the 2013 dengue outbreak in Cali, Colombia.

Conclusions:

  • The study provides a framework for understanding and managing epidemic peaks.
  • Viability kernels offer insights into epidemic control strategies under resource constraints.
  • Mathematical modeling is crucial for predicting and mitigating disease outbreaks.