Annealed mean-field epidemiological model on scale-free networks with a mitigating factor

TL;DR

This paper introduces an annealed mean-field epidemic model on scale-free networks, analyzing infection thresholds and mitigation effects, revealing that mitigation significantly reduces encounter probabilities without affecting prevalence trends.

Contribution

The study develops a novel annealed mean-field model incorporating mitigation factors on scale-free networks, providing analytical insights into epidemic thresholds and prevalence behavior.

Findings

Mitigation drastically reduces the probability of encountering infected individuals.

Stationary prevalence remains monotonically increasing with infection rate despite mitigation.

Model offers analytical and numerical understanding of epidemic dynamics on sparse scale-free networks.

Abstract

An annealed version of the quenched mean-field model for epidemic spread is introduced and investigated analytically and assisted by numerical calculations. The interaction between individuals follows a prescription that is used to generate a scale-free network, and we have adjusted the number of connections to produce a sparse network. Specifically, the model's behavior near the infection threshold is examined, as well as the behavior of the stationary prevalence and the probability that a connection between individuals encounters an infected one. We found that these functions display a monotonically increasing dependence on the infection rate. Subsequently, a modification that mimics the mitigation in the probability of encountering an infected individual is introduced, following an old idea rooted in the Malthus-Verhulst model. We found that this modification drastically changes the probability that a connection meets an infected individual. However, despite this change, it does not alter the monotonically increasing behavior of the stationary prevalence.