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A delay model for persistent viral infections in replicating cells.

Hayriye Gulbudak1, Paul L Salceanu2, Gail S K Wolkowicz3

  • 1Mathematics Department, University of Louisiana at Lafayette, Lafayette, LA, USA. hayriye.gulbudak@louisiana.edu.

Journal of Mathematical Biology
|May 16, 2021
PubMed
Summary
This summary is machine-generated.

This study models persistent viral infections in replicating cells, revealing how factors like the eclipse stage duration influence long-term virus survival and population dynamics.

Keywords:
Backward bifurcationBistable dynamicsBogdanov–Takens bifurcationChronically infecting phagePersistent viral infectionRobust uniform persistenceStability analysis

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Area of Science:

  • Virology
  • Mathematical Biology
  • Dynamical Systems

Background:

  • Persistent viral infections involve viruses residing in host cells long-term without immediate cell death.
  • This long-term survival is crucial for viruses like HIV, in oncolytic virotherapy, and in microbial hosts with non-virulent phages.
  • Understanding these dynamics requires mathematical modeling of viral replication within cell populations.

Purpose of the Study:

  • To develop and analyze a mathematical model for persistent viral infection in a replicating cell population.
  • To investigate the role of the eclipse stage time delay on viral persistence and population dynamics.
  • To identify conditions for long-term virus survival using concepts like robust uniform persistence.

Main Methods:

  • A mathematical model incorporating a time delay in the eclipse stage of viral infection was developed.
  • Reproduction numbers were calculated to determine the existence and stability of system equilibria.
  • Bifurcation analysis (transcritical, saddle-node, Hopf, homoclinic, Bogdanov-Takens) and numerical continuation were employed.
  • Parameter space was explored using two-parameter bifurcation diagrams.

Main Results:

  • The study identified criteria for the existence and stability of different system states (equilibria).
  • Various bifurcation phenomena were observed, indicating complex dynamical behaviors.
  • Robust uniform persistence was used to confirm the possibility of long-term infection survival.
  • Two-parameter bifurcation diagrams revealed distinct regions of dynamical outcomes based on parameter variations.

Conclusions:

  • The duration of the eclipse stage significantly impacts viral survival and population dynamics.
  • Mathematical modeling provides crucial insights into the complex dynamics of persistent viral infections.
  • The findings have implications for understanding viral persistence in various biological contexts, including disease reservoirs and therapeutic strategies.