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An epidemic dynamics model with limited isolation capacity.

Ishfaq Ahmad1, Hiromi Seno2

  • 1Department of Computer and Mathematical Sciences, Graduate School of Information Sciences, Tohoku University, Aramaki-Aza-Aoba 6-3-09, Aoba-ku, Sendai, Miyagi, 980-8579, Japan. ishfaqmaths899@gmail.com.

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Limited isolation capacity can drastically increase epidemic size. Maintaining sufficient isolation capacity is crucial to prevent severe outbreaks and manage the final epidemic size effectively.

Keywords:
Epidemic dynamicsFinal epidemic sizeIsolationMathematical modelOrdinary differential equations

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Area of Science:

  • Epidemiology
  • Mathematical Biology
  • Public Health Modeling

Background:

  • Understanding epidemic dynamics is crucial for public health interventions.
  • Limited resources, such as isolation capacity, can significantly impact disease spread.
  • Previous models often assume unlimited isolation capabilities.

Purpose of the Study:

  • To investigate the impact of finite isolation capacity on the final epidemic size.
  • To identify conditions under which isolation capacity is reached during an epidemic.
  • To analyze the relationship between isolation capacity and epidemic severity.

Main Methods:

  • Utilized a modified SIR (Susceptible-Infectious-Recovered) model.
  • Employed a four-dimensional system of ordinary differential equations.
  • Derived conditions for isolation capacity being reached in finite time.

Main Results:

  • Final epidemic size decreases monotonically with increasing isolation capacity.
  • A critical isolation capacity exists where the final epidemic size can change discontinuously.
  • Exceeding isolation capacity leads to a drastic increase in the total number of infected individuals.

Conclusions:

  • Breakdown of limited isolation capacity can cause severe, unexpected epidemic situations.
  • Sufficient isolation capacity is essential for mitigating epidemic spread and severity.
  • The findings highlight the importance of resource allocation in epidemic preparedness.