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Stability analysis of within-host parasite models with delays
Abderrahman Iggidr1, Joseph Mbang, Gauthier Sallet
1INRIA-Lorraine and University Paul Verlaine-Metz LMAM-CNRS UMR 7122, ISGMP Bat. A, Ile du Saulcy 57045 Metz Cedex 01, France. iggidr@loria.fr
This study analyzes within-host parasitic infections with distributed delays. The basic reproduction ratio (R0) determines parasite clearance or endemic stability, with R0>1 indicating stability in many models.
Area of Science:
- Mathematical Biology
- Parasitology
- Epidemiology
Background:
- Within-host parasitic infections are complex, involving latent stages and varying target cell infection times.
- Understanding the dynamics of these infections is crucial for developing effective treatments.
Purpose of the Study:
- To globally analyze mathematical models of within-host parasitic infections.
- To investigate the role of distributed delays in parasitic infection dynamics.
- To compute and interpret the basic reproduction ratio (R0) for these systems.
Main Methods:
- Analysis of systems with parallel classes of latently infected target cells.
- Modeling parasitic infections with distributed continuous delays.
- Computation of the basic reproduction ratio (R0).
- Determination of global asymptotic stability (GAS) conditions.
Main Results:
- Parasite clearance occurs when R0 ≤ 1.
- Global asymptotic stability of the endemic equilibrium is achieved when R0 > 1, provided a sufficient condition is met.
- For certain models, the condition for stability simplifies to R0 > 1.
Conclusions:
- The findings provide a framework for analyzing parasitic infections with intracellular delays.
- This work contributes to understanding the global stability of endemic equilibria in parasitic systems.
- The basic reproduction ratio is a key determinant of infection persistence or clearance.
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