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The dynamics of vector-borne relapsing diseases.

Cody Palmer1, Erin Landguth2, Emily Stone1

  • 1Department of Mathematical Sciences, University of Montana, USA.

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|January 18, 2018
PubMed
Summary

This study models vector-borne relapsing diseases, like tick-borne relapsing fever. Mathematical analysis confirms disease spread dynamics and stability near the critical threshold (R₀=1), with no backward bifurcation observed.

Keywords:
Compartmental modelsEpidemiologyLouse-borne relapsing feverReproductive numberTick-borne relapsing fever

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Area of Science:

  • Epidemiology
  • Mathematical Biology
  • Disease Dynamics

Background:

  • Vector-borne relapsing diseases pose significant public health challenges.
  • Understanding disease transmission dynamics is crucial for effective control strategies.
  • Compartmental models are valuable tools for analyzing infectious disease spread.

Purpose of the Study:

  • To mathematically model the dynamics of vector-borne relapsing diseases.
  • To analyze the stability of disease-free and endemic equilibria.
  • To investigate the impact of relapses on disease transmission and stability.

Main Methods:

  • Utilized compartmental modeling to represent disease transmission.
  • Derived and proved the general form of the basic reproductive number (R₀).
  • Analyzed bifurcations at the disease-free equilibrium, specifically transcritical bifurcations.

Main Results:

  • The disease-free equilibrium undergoes a transcritical bifurcation at R₀=1.
  • A single branch of endemic equilibria is locally asymptotically stable for R₀ close to 1.
  • Demonstrated the absence of backward bifurcation, regardless of the number of relapses.

Conclusions:

  • The model provides robust insights into the epidemiological dynamics of relapsing vector-borne diseases.
  • The stability analysis confirms predictable disease persistence under certain conditions.
  • Findings are extendable to models with variable relapse numbers, offering broader applicability.