[2111.05590] 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 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.