Estimating epidemic arrival times using linear spreading theory.

Area of Science:

• Epidemiology
• Network Science
• Mathematical Modeling

Background:

• Global epidemics spread through interconnected populations.
• Predicting disease arrival times is crucial for public health interventions.
• Existing models often lack spatial structure or network dynamics.

Purpose of the Study:

• To develop and validate a spatially structured model for predicting worldwide epidemic dynamics.
• To formulate accurate predictions for disease arrival times in different cities.
• To compare predictions from linearized and nonlinear epidemic models.

Main Methods:

• Utilized a meta-population susceptible-infected-recovered (SIR) compartmental model on a network of cities and flight paths.
• Employed a linearized system derived from ordinary differential equations to analyze spreading speeds and arrival times.
• Developed two prediction methods: one based on heat kernel expansion and another assuming simplified transmission pathways (1D lattice or homogeneous tree).

Main Results:

• The linearized model's predictions for arrival times were compared to the nonlinear system's dynamics.
• The heat kernel expansion method and the simplified pathway approximation yielded comparable arrival time predictions.
• Predictions were tested and validated using a real-world network of global airline traffic.

Conclusions:

• Spatially structured epidemic models can accurately predict disease arrival times.
• Linearized models offer a computationally efficient approach for forecasting epidemic spread.
• Network topology and transmission pathways significantly influence epidemic dynamics and arrival times.