Abstract To investigate the influences of heterogeneity and waning immunity on measles transmission. we formulate a network model with periodic transmission rate. and theoretically examine the threshold dynamics. We numerically find that the waning of immunity can lead to an increase in the basic reproduction number R 0 $R_{0}$ and the density of infected individuals. https://parisnaturalfoodes.shop/product-category/nutri-nac-600-mg/