Insecticide-treated nets (ITNs) are at the forefront of malaria control programs and even though the percentage of households in sub-Saharan Africa that owned nets increased from 3% in 2000 to 53% in 2012, many children continue to die from malaria. The potential impact of ITNs on reducing malaria transmission is limited due to inconsistent or improper use, as well as physical decay in effectiveness. Most mathematical models for malaria transmission have assumed a fixed effectiveness rate for bed-nets, which can overestimate the impact of nets on malaria control. We develop a model for malaria spread that captures the decrease in ITN effectiveness due to physical and chemical decay, as well as human behavior as a function of time. We perform uncertainty and sensitivity analyses to identify and rank parameters that play a critical role in malaria transmission. These analyses show that the basic reproduction number R0, and the infectious human population are most sensitive to bed-net coverage and the biting rate of mosquitoes. Our results show the existence of a backward bifurcation for the case in which ITN efficacy is constant over time, which occurs for some range of parameters and is characterized by high malaria mortality in humans. This result implies that bringing R0 to less than one is not enough for malaria elimination but rather additional efforts will be necessary to control the disease. For the case in which ITN efficacy decays over time, we determine coverage levels required to control malaria for different ITN efficacies and demonstrate that ITNs with longer useful lifespans perform better in malaria control. We conclude that malaria control programs should focus on increasing bed-net coverage, which can be achieved by enhancing malaria education and increasing bed-net distribution in malaria endemic regions.