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

Motivated by the increasing number of COVID-19 cases that have been observed in many countries after the vaccination campaign and relaxation of non-pharmaceutical interventions (NPIs), we propose a network model for the spread of recurrent epidemic diseases in a partially vaccinated population. The model encapsulates several realistic features, such as different vaccine efficacy against transmission and development of severe symptoms, testing practices, implementation of NPIs, 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 below 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 towards 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, favouring resurgent outbreaks, and it thus calls for higher testing rates, more cautiousness and responsibility among the population, or the reintroduction of NPIs to achieve full eradication.