Modelling behavioural changes and vaccination in the transmission of respiratory viruses with co-infection

We consider a mathematical model to explore the effects of human behavioural changes on the transmission of two respiratory viruses, where co-infection is possible. The model includes an index to describe the human choices induced by information and rumours regarding the diseases. We first consider the case in which the public health authorities rely only on non-pharmaceutical containment measures and perform a qualitative analysis of the model through bifurcation theory, in order to analyse the existence and stability of both endemic and co-endemic equilibria. We also show the impact of the most relevant information-related parameters on the system dynamics. Then, we extend the model by assuming that a vaccine is available for each of the two viruses. We show how adherence to social distancing may be affected by information and rumours regarding the vaccination coverage in the community. Finally, we investigate the effects of seasonality by introducing a two-state switch function to represent a reduction in both vaccination and transmission rates during the summer season. We found that seasonality causes an increase in the prevalence peaks, suggesting that the detrimental effects due to the reduction of vaccination rates prevail over the beneficial ones due to the reduction of transmission.