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A Theoretical Analysis of Mass Testing Strategies to Control Epidemics.

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Test-and-isolate policies can effectively contain COVID-19 epidemics. This study provides theoretical conditions for epidemic extinction using SIR and SEIR models with testing and isolation strategies.

Keywords:
Eigenvalues of integral operatorsEpidemic modelImpulsive differential equationsMass testing strategyReproduction number

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Area of Science:

  • Epidemiology
  • Mathematical Modeling
  • Public Health Interventions

Background:

  • COVID-19 containment strategies often include test-and-isolate policies.
  • Previous analyses primarily used simulation models, lacking theoretical frameworks for simple epidemic models.

Purpose of the Study:

  • To theoretically analyze the effectiveness of test-and-isolate strategies in simple epidemic models.
  • To determine conditions for epidemic extinction under these policies.
  • To define and compute the effective reproduction number () for these models.

Main Methods:

  • Developed four epidemic models (SIR and SEIR types) incorporating periodic testing and isolation of positive cases.
  • Derived analytical and numerical methods to compute the effective reproduction number ().
  • Investigated conditions for disease extinction based on model parameters.

Main Results:

  • Established conditions under which test-and-isolate strategies can lead to epidemic extinction.
  • Provided a computable definition for the effective reproduction number () in the context of these interventions.
  • Demonstrated numerically that the final-size relation of SIR models is approximately maintained across the studied models.

Conclusions:

  • Test-and-isolate policies, when theoretically analyzed within SIR/SEIR frameworks, offer a viable strategy for epidemic control.
  • The study provides a mathematical basis for understanding the efficacy of such public health measures.
  • The findings support the use of these policies in managing infectious disease outbreaks.