Malaria is a deadly infectious disease, which is transmitted to humans via the bites of infected female mosquitoes. Antimalarial drug resistance has been identified as one of the characteristics of malaria that complicates control efforts. Typically, the use of insecticide-treated bed-nets (ITNs) and drug treatment are some of the recommended control strategies against malaria. Here, the use of ITNs, drug treatment, and their efficacies and evolution of antimalarial drug resistance are considered to be the major driving forces in the dynamics of malaria transmissions. We formulate a mathematical model of two-strain malaria to assess the impacts of ITNs, drug treatment, and their efficacies on the transmission dynamics of the disease in a human population. We propose a simple mosquito biting rate function that depends on both the proportion of ITN usage and its efficacy. We show that both disease-free and co-existence equilibrium points are globally-asymptotically stable where they exist. The global uncertainty and sensitivity analysis conducted show that if about 95% of malaria cases can be treated with fewer than 5% treatment failure in a population with 95% ITN usage that remains 95% effective, malaria can be controlled. We find that the order in which numerous intervention measures are taken is important.
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