Reducing the basic reproduction number below a certain threshold is necessary for containing the disease. Thus, it is important to identify and classify model parameters that can be used to bring down the basic reproduction number. To this effect, we carried out both a local and a global sensitivity analysis to understand the impact of various model parameters on the basic reproduction number. We found out for both the local and global sensitivity analyses that the basic reproduction number is most sensitive to the probability that a questing mosquito succeeds in acquiring a blood meal, the probability that a successfully fed mosquito returns safely to a breeding site, the ITN coverage and the probability that a questing mosquito prefers to feed on a susceptible human. Global uncertainty and sensitivity analyses were carried out to assess the contributions of the parameters of the model to the infectious and partially immune human populations for both the autonomous and non-autonomous models; i.e., the model for which ITN efficacy is constant over time and that for which ITN efficacy is allowed to wane over time. Our results indicate that the same parameters that the basic reproduction number is most sensitive to are the key model parameters, not only because they contribute most in influencing the infectious and partially immune human populations, but also because they are important control parameters through which the use of ITNs can impact disease prevalence. These parameters include the probability that a mosquito is successful in feeding on a human pw, the probability that a successfully fed mosquito returns to a breeding site θw, the ITN coverage b0, the birth rate of mosquitoes λm, the attraction rate of infectious mosquitoes to humans αu, and the maximum biting rate of mosquitoes βmax.