Dynamical analysis of an age-structured multi-group SIVS epidemic model.

Host heterogeneities such as space, gender, and age etc are intrinsic characters for investigating diseases mechanisms and transmission routes. First, we incorporate inter-group, intra-group and age structure to propose a multi-group SIVS epidemic model. Then we obtain the basic reproduction number of the system which is the spectral radius of the next generation operator by the renewal equation. Based on some assumptions for parameters, we obtain the existence and uniqueness of endemic equilibrium. By means of integral semigroup theory and Lyapunov methods, we show that the threshold dynamics of the system is completely determined by the basic.