Pattern dynamics analysis and parameter identification of spatiotemporal infectious disease models on complex...

Area of Science:

• Mathematical Biology
• Network Science
• Epidemiology

Background:

• Reaction-diffusion systems are fundamental to modeling spatial phenomena.
• Advection and time delays significantly influence system dynamics, particularly in biological contexts.
• Network structures provide a framework for understanding complex interactions in disease transmission.

Purpose of the Study:

• To investigate reaction-diffusion systems with advection on discrete networks.
• To develop an infectious disease transmission model incorporating time delays.
• To analyze the impact of network topology and advection on disease dynamics.

Main Methods:

• Analysis of equilibrium point existence and linear approximation of time delays.
• Determination of Turing instability conditions.
• Construction of lower-order and higher-order network structures.
• Application of optimal control for parameter identification.
• Extensive numerical simulations.

Main Results:

• Identified conditions for equilibrium and Turing instability.
• Demonstrated the influence of advection and network order on system dynamics.
• Successfully applied optimal control for parameter identification in complex networks.
• Validated the model's effectiveness for real-world data fitting and prediction.

Conclusions:

• Advection and higher-order networks play crucial roles in shaping disease transmission dynamics.
• The developed model effectively captures complex spatio-temporal patterns.
• The methodology provides a robust framework for epidemiological modeling and prediction.