Improving pairwise approximations for network models with susceptible-infected-susceptible dynamics

Area of Science:

• Epidemiology
• Network Science
• Mathematical Biology

Background:

• Network models are crucial for understanding epidemic dynamics, especially for diseases with long-lasting contacts.
• Standard moment-closure approximations, like pairwise approximation, are effective for SIR dynamics but less so for SIS dynamics where network structure is critical.
• Sexually transmitted infections (STIs) often follow SIS dynamics and are influenced by rare, long-term contacts, highlighting the need for improved network modeling.

Purpose of the Study:

• To introduce an improved pairwise approximation for network models of SIS dynamics.
• To enhance the accuracy of epidemic modeling on specific network structures by addressing errors in standard approximations.
• To provide a more refined understanding of how network structure impacts SIS epidemic dynamics.

Main Methods:

• Developed an improved pairwise approximation by tracking the rate of change of errors between triple and pairwise values.
• Applied the improved method to two network structures: the isolated open triple and k-regular networks.
• For k-regular networks, a closure at the triple level was implemented to create a closed set of equations.

Main Results:

• The improved pairwise model is exact for the isolated open triple network structure.
• For k-regular networks, the closure at the triple level yields a more accurate model.
• The enhanced model provides insight into standard pairwise approximation errors and closely matches higher-order methods and simulations with minimal dimensionality increase.

Conclusions:

• The improved pairwise approximation offers a more accurate representation of SIS dynamics on networks compared to the standard method.
• This approach enhances the understanding of network structure's impact on STIs and similar diseases.
• The method presents a valuable tool for epidemiological modeling, balancing accuracy and computational complexity.