Epidemics with mutating infectivity on small-world networks

Area of Science:

• Epidemiology
• Evolutionary Biology
• Network Science

Background:

• Pathogen epidemics and evolution often occur concurrently, entangling their dynamics.
• The spatial spread of infectious diseases across interconnected hosts, like cities, is a critical factor in epidemic progression.

Purpose of the Study:

• To theoretically investigate the impact of mutations that increase infection rates on epidemic dynamics within networks.
• To analyze how network structure, particularly the small-world property, influences the interplay between mutation and disease spread.

Main Methods:

• Analysis of the SIR (Susceptible-Infected-Recovered) model on grid-like networks with varying connectivity.
• Modeling pathogen spread with mutations affecting infection rates, considering both discrete and continuous genetic changes.
• Derivation and solution of a Fokker-Planck-like equation for continuous mutations using WKB approximation for small numbers of long-range connections.

Main Results:

• Small-world networks, characterized by long-range connections, increase vulnerability to supercritical mutations, potentially escalating outbreaks.
• An increase in the number of long-range links can reverse this effect, leading to a decreased probability of large-scale epidemics.
• Mutations potentiating transmissibility can emerge during an epidemic wave, not solely preceding it.

Conclusions:

• Network topology significantly modulates the effect of beneficial mutations on epidemic outbreaks.
• The timing and impact of transmissibility-enhancing mutations are influenced by the underlying host network structure.
• Understanding these dynamics is crucial for predicting and managing infectious disease spread in interconnected populations.