Although neutron-induced activation in a fusion reactor is a nonlinear problem whose solution requires the use of both neutron transport and activation codes, a simplified analytical approach to bismuth and polonium build-up in lead is proposed to estimate the polonium inventory and the related biological hazards of LiPb-bearing blankets. All neutronic reactions of polonium build-up in lead and in its bismuth impurities are surveyed and discussed. The contribution of the different possible chains to the build-up of polonium is evaluated. A set of differential equations for the densities of 209Bi and 210Po isotopes in the lead is worked into simplified, easy-to-use expressions. These analytical formulas obtained for the densities can be used for the estimation of both the bismuth and the polonium densities after any reactor operation time and allow identification of the build-up mechanisms of those isotopes. A simplified formula for polonium inventory estimations at any blanket zone is proposed as well. The polonium inventory evaluation takes into account the initial conditions (primarily bismuth impurity in the lead) and the reactor operation conditions, such as the average availability of a fusion reactor and the blanket operation scenario.