When ITN efficacy wanes over time, we used the approach for computing the basic reproduction numbers of time-periodic systems in Wang and Zhao (2008) to explore the impact of ITN coverage and the mosquito attraction and feeding preferences on the basic reproduction number and disease prevalence. We found out that in areas with low mosquito densities where mosquitoes do not also bite frequently, approximately 83–88% ITN coverage is required to contain malaria. However, in areas with high mosquito densities or where mosquitoes bite frequently, ITNs must be complemented with other mitigation strategies to bring the disease under control. This is very common in areas in which malaria is highly endemic such as some sub-Saharan African countries. Complementary malaria control measures include indoor residual spraying, the use of prophylactic drugs, intermittent preventive treatment in pregnant women, etc. Our results reveal that the basic reproduction numbers of the models with constant or averaged ITN efficacy underestimate disease transmission risk. We also found out that depending on whether the area of study has high or low mosquito densities, the malaria disease can be controlled if (1) 7–18% of mosquitoes are attracted to susceptible humans; (2) infectious mosquitoes are 0.5–0.9 times attracted to humans; or (3) mosquitoes are 21–30 times more likely to feed on infectious humans or 8.2–13 times more likely to feed on partially immune humans. This calls for more field work to better understand the attraction of feeding preference exhibited by various classes of mosquitoes to different classes of humans. In particular, although there is some limited empirical evidence suggesting that mosquitoes are more attracted to infectious humans than susceptible humans (Lacroix et al., 2005) and that infectious mosquitoes are more attracted to humans than susceptible mosquitoes (Smallegange et al., 2013), our study reveals that there is need for more field studies to investigate these further and to investigate whether there is empirical evidence to suggest that infectious mosquitoes are more attracted to susceptible humans than to infectious humans, while susceptible mosquitoes are more attracted to infectious or partially immune humans than to susceptible humans. These two situations will amplify disease prevalence. A better understanding of the impacts of these biased preferences can lead to the design and implementation of better disease control measures. Our analysis also reveals that ITNs perform best when they are replaced within shorter time periods compared to when they are replaced after longer time periods, and that in areas with very high mosquito densities, replacing ITNs after the 3-year useful life prescribed by WHO might not be enough to contain the disease. As in Ngonghala et al. (2014), we found out that introducing ITNs with longer lifespans are better suited for malaria control than those with shorter lifespans.