Spatial structure and fluctuations in the contact process and related models.

Area of Science:

• Mathematical modeling
• Statistical physics
• Computational biology

Background:

• The contact process is a fundamental spatial model used across various scientific fields.
• Analytical solutions for the contact process are challenging due to complex spatial correlations.
• Existing approximations, like pair approximations, have limitations in accurately capturing dynamics.

Purpose of the Study:

• To introduce a novel, empirically based approximate method for characterizing spatial correlations in the contact process.
• To simplify the analysis of spatiotemporal dynamics by converting the problem into a temporal one.
• To improve the accuracy of predictions for equilibrium population, variance, and first passage times.

Main Methods:

• Developed an approximate method using a single adjustable parameter to capture spatial correlations.
• Recast the contact process as a stochastic birth-death process.
• Applied the method to predict equilibrium population, population variance, and first passage time distributions.

Main Results:

• The new method provides more accurate predictions of equilibrium population compared to pair approximations.
• Achieved good predictions for population variance.
• Demonstrated good predictions for first passage time distributions to low thresholds.
• The approach is generalizable to other models with mixed interaction types.

Conclusions:

• The introduced approximation effectively simplifies the analysis of the contact process.
• This method offers a significant improvement in predicting key population dynamics.
• The approach has broad applicability to other spatiotemporal models with global and nearest-neighbor interactions.