Immunization of networks with limited knowledge and temporary immunity

Area of Science:

• Statistical Physics
• Network Science
• Complex Systems

Background:

• Network resilience and epidemic spreading models traditionally rely on random node/edge removal or immunization.
• Existing models often lack the ability to account for targeted strategies and temporary immunity in complex networks.

Purpose of the Study:

• To develop a theoretical framework for targeted immunization strategies in networks with limited observation.
• To analyze the impact of temporary immunity and its decay on network percolation properties.
• To uncover distinct behaviors of Erdős-Rényi and power-law networks under these conditions.

Main Methods:

• Developed a theoretical framework for targeted immunization where the most connected node within a sample of 'n' nodes is immunized.
• Introduced a decay probability 'ρ' to model the loss of immunity over time.
• Performed analytical examination of percolation properties and scaling laws for different network types (Erdős-Rényi, power-law).

Main Results:

• Identified distinctive percolation properties and scaling laws for Erdős-Rényi and power-law networks based on 'n' and 'ρ'.
• Analyzed scenarios with both fixed immunity loss rates and asymptotic total loss.
• Demonstrated how limited knowledge and temporary immunity significantly alter network dynamics.

Conclusions:

• The proposed framework provides a novel approach to studying targeted immunization with temporary immunity in complex networks.
• Findings highlight the importance of considering observation limitations and immunity decay for realistic epidemic modeling.
• This work paves the way for understanding complex percolation processes with dynamic and partial protection.