Global stability for epidemic models on multiplex networks
Yu-Jhe Huang1, Jonq Juang2, Yu-Hao Liang1
1Department of Applied Mathematics, National Chiao Tung University, Hsinchu, Taiwan.
Journal of Mathematical Biology
|September 9, 2017
Summary
This study models epidemics on multiplex networks, examining disease spread in physical layers alongside information diffusion in virtual layers. Key reproduction numbers determine disease extinction or outbreak based on transmission dynamics.
Area of Science:
- Epidemiology
- Network Science
- Mathematical Modeling
Background:
- Real-world systems often involve interconnected layers, such as physical and social networks.
- Understanding disease dynamics requires considering simultaneous processes like infection and information spread.
- Multiplex networks, with coupled layers, present unique challenges for epidemic modeling.
Purpose of the Study:
- To develop and analyze an epidemic model on a two-layer multiplex network.
- To investigate the interplay between disease transmission (physical layer) and information diffusion (virtual layer).
- To define and analyze basic reproduction numbers for both layers and their impact on epidemic outcomes.
Main Methods:
- Mathematical modeling of a susceptible-infected-susceptible (SIS) process in the physical layer.
- Modeling of an unaware-aware-unaware (UAU) cyclic process in the virtual layer.
- Analytical derivation and numerical analysis of basic reproduction numbers (R0) for both layers.
- Stability analysis of equilibrium points (disease-free and information-saturated states).
Main Results:
- Analytical conditions established for global stability of disease-free and information-free equilibrium when both R0 values are below critical thresholds.
- Analytical conditions established for global stability of disease-free and information-saturated equilibrium when both R0 values exceed critical thresholds.
- Numerical simulations demonstrate that when one R0 is below its threshold, disease extinction depends on the competition between information transmission and disease contagiousness.
Conclusions:
- The model provides insights into disease dynamics on multiplex networks, highlighting the dual role of information spread.
- The interplay between physical and virtual layer dynamics significantly influences epidemic outcomes.
- Specific conditions involving reproduction numbers and transmission rates determine whether a disease dies out or becomes endemic.
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