Modelling the Effect of Vaccination and Human Behaviour on the Spread of Epidemic Diseases on Temporal Networks

TL;DR

This paper presents a mathematical model on temporal networks to analyze how vaccination, human behavior, and testing practices influence the spread of epidemic diseases, highlighting the importance of cautious behavior and interventions.

Contribution

It introduces a comprehensive time-varying network model incorporating vaccination, testing, and human behavior, with analytical derivation of epidemic thresholds and prevalence.

Findings

Precautious human behavior and testing are crucial to prevent outbreaks.

Vaccination reduces severe cases but may sometimes promote resurgences.

Higher testing and non-pharmaceutical interventions are necessary for eradication.

Abstract

Motivated by the increasing number of COVID-19 cases that have been observed in many countries after the vaccination and relaxation of non-pharmaceutical interventions, we propose a mathematical model on time-varying networks for the spread of recurrent epidemic diseases in a partially vaccinated population. The model encapsulates several realistic features, such as the different effectiveness of the vaccine against transmission and development of severe symptoms, testing practices, the possible implementation of non-pharmaceutical interventions to reduce the transmission, isolation of detected individuals, and human behaviour. Using a mean-field approach, we analytically derive the epidemic threshold of the model and, if the system is above such a threshold, we compute the epidemic prevalence at the endemic equilibrium. These theoretical results show that precautious human behaviour and effective testing practices are key toward avoiding epidemic outbreaks. Interestingly, we found that, in many realistic scenarios, vaccination is successful in mitigating the outbreak by reducing the prevalence of seriously ill patients, but it could be a double-edged sword, whereby in some cases it might favour resurgent outbreaks, calling for higher testing rates, more cautiousness and responsibility among the population, or the reintroduction of non-pharmaceutical interventions to achieve complete eradication.