Modelling and analysis of global resurgence of mumps: A multi-group epidemic model with asymptomatic infection, general vaccinated and exposed distributions

Based on the possible mechanism of the recent global resurgence of mumps, a novel multi-group SVEIAR epidemic model with infinite distributed delays of vaccination and latency, asymptomatic infection and nonlinear incidence is formulated, which is also equivalent to the multi-group version with ages of vaccination and latency. Here, it is assumed that the vaccine confers complete protection against infection. By constructing Lyapunov functionals, it is shown that the disease will die out if the vaccinated reproduction number Rv≤1 and the disease becomes endemic if Rv>1. Moreover, the threshold dynamics of the multi-group SVEIAR epidemic model of ordinary differential equations (ODEs) with imperfect vaccination is also established. Our main conclusions generalize and improve some existing results. In the end, it is found that the possible reasons for occurrence of backward bifurcation in epidemic models with vaccination may include partial immunity, standard incidence by comparing our results obtained with the existing literatures.