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Multiscale model within-host and between-host for viral infectious diseases.
Alexis Erich S Almocera1, Van Kinh Nguyen1, Esteban A Hernandez-Vargas2
1Frankfurt Institute for Advanced Studies, Ruth-Moufang-Straße 1, 60438, Frankfurt am Main, Germany.
Journal of Mathematical Biology
|May 9, 2018
Summary
This study analyzes multiscale infectious disease models. We found that viral load influences disease transmission, with a Michaelis-Menten function better representing scale-bridging than a proportional function.
Area of Science:
- Epidemiology
- Mathematical Biology
- Infectious Disease Modeling
Background:
- Multiscale models offer novel insights into infectious disease dynamics.
- Understanding within-host and between-host interactions is crucial for disease control.
Purpose of the Study:
- To perform a rigorous stability analysis of a coupled multiscale infectious disease model.
- To investigate the relationship between within-host viral load and between-host transmission.
- To determine the impact of the coupling function on model behavior.
Main Methods:
- Stability and bifurcation analyses were applied to within-host and between-host subsystems.
- Coupling of the basic reproduction numbers (R0_within and R0_between) was analyzed.
- Lyapunov functions were used to establish global stability for the between-host system.
- Numerical simulations compared different functional forms for viral load-dependent transmission.
Main Results:
- Local stability of each subsystem was confirmed, aligning with classical control approaches.
- Global stability of the between-host system was demonstrated.
- The basic reproduction number for the between-host system (R0_between) was shown to be an increasing function of the within-host basic reproduction number (R0_within).
- A Michaelis-Menten function, rather than a directly proportional function, better described the relationship between scales.
Conclusions:
- The study provides fundamental understanding of coupled within-host and between-host models.
- The choice of coupling function significantly impacts the linkage between different scales of disease dynamics.
- Findings inform the development of more accurate infectious disease models.
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