I will present some recent work of Mbi based group which investigated a mathematical model of a large pandemic,  leading to the Law of Large number result for the SIR type epidemics on random contact networks.   I will also discuss the applications of the LLN approximation in building a "network-free" SIR Markov hybrid model which can be used for epidemic parameters inference. The hybrid model idea appears particularly relevant in the context of the recent Ebola and the current Zika virus epidemics.