We showed that when the efficacy of ITNs is constant over time and there is no disease, a threshold parameter Rm, referred to as the vectorial reproduction number exists, and that this threshold can be used to characterize the nonexistence of mosquitoes when it is less than or equal to unity or the existence of mosquitoes when it is bigger than unity. The size of Rm is determined by a number of key parameters including the mosquito birth rate, the probability that a mosquito succeeds in taking a blood meal, and the probability that a successfully fed mosquito returns to the breeding site. We demonstrated that there is a globally stable mosquito-free equilibrium when Rm1. Thus, it is possible to reduce the mosquito population to an acceptable ecological level, even when there is no disease in the population simply by using ITNs, as reflected by the impacts of the key parameters involved in the expression for Rm.