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A two-dimensional discrete delay-differential system model of viremia
Joseph E Carroll1,2,3
1Department of Mathematics, California State Polytechnic University, Humboldt.
Mathematical Biosciences and Engineering : MBE
|September 20, 2022
Summary
This study models virus-immune system interactions using delay-differential equations. Model parameters can predict if a virus will persist or be cleared by the immune system.
Area of Science:
- Mathematical biology
- Immunology
- Virology
Background:
- Viral infections pose significant public health challenges.
- Understanding the dynamics of virus-immune system interactions is crucial for developing effective treatments.
- Circulating target cells are key in many viral disease progressions.
Purpose of the Study:
- To develop a deterministic mathematical model for virus-immune system dynamics.
- To analyze the long-term behavior of viral persistence or extinction.
Main Methods:
- A system of two ordinary first-order quadratic delay-differential equations was formulated.
- The model's coefficients were set to become constant, leading to an autonomous system.
- Long-term solution behavior was investigated through parameter analysis.
Main Results:
- Two key functions of model parameters were identified.
- The signs of these functions often predict viral persistence or extinction.
- The predictive power of these functions is not absolute.
Conclusions:
- The developed model offers insights into virus-immune system dynamics.
- Parameter analysis can guide predictions of viral fate.
- Further refinement may enhance the model's predictive accuracy.
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