Malaria prevalence in sub-Saharan Africa remains high. Kenya for example, records about 3.5 million new cases and 11 thousand deaths each year.1 Most of these cases and deaths are among children under five. The main control method in malaria endemic regions has been through the use of insecticide-treated nets (ITNs). Although this approach has been fairly successful, the gains are threatened by mosquito-resistance to pyrethroids (insecticides on nets), physical and chemical degradation of ITNs that reduce their efficacy, inconsistent and improper use by humans, etc. We present a model to investigate the effects of ITN use and mosquito-resistance and adaptation to pyrethroids used to treat bed nets on malaria prevalence and control in malaria endemic regions. The model captures the development and loss of resistance to insecticides, the effects of ITN use on malaria control in a setting where proper and consistent use is not guaranteed, as well as differentiated biting of human hosts by resistant and sensitive mosquitoes. Important thresholds, including the basic reproduction number [Formula: see text], and two parameter groupings that are important for disease control and for establishing the existence of endemic equilibria to the model are calculated. Furthermore, a global sensitivity analysis is carried out to identify important parameters such as insecticide treated bed-net coverage, ITN, the maximum biting rate of resistant mosquitoes, etc., that drive the system and that can be targeted for disease control. Threshold levels of ITN coverage and ITN efficacy required for containing the disease are identified and shown to depend on the type of insecticide-resistance. For example, when mosquito-resistance to insecticides is not permanent and is acquired only through recruitment and the efficacy of ITNs is [Formula: see text], about [Formula: see text] net coverage is required to contain malaria. However, for the same ITN efficacy, i.e., [Formula: see text], approximately [Formula: see text] net coverage is required to contain the disease when resistance to insecticides is permanent and is acquired through recruitment and mutation in mosquitoes. The model exhibits a backward bifurcation, which implies that simply reducing [Formula: see text] slightly below unity might not be enough to contain the disease. We conclude that appropriate measures to reduce or eliminate mosquito-resistance to insecticides, ensure that more people in endemic areas own and use ITNs properly, and that the efficacy of these nets remain high most of the time, as well as educating populations in malaria endemic areas on how to keep mosquito densities low and minimize mosquito bites are important for containing malaria.

Malaria prevalence in sub-Saharan Africa remains high. Kenya for example, records about 3.5 million new cases and 11 thousand deaths each year [1]. Most of these cases and deaths are among children under five. The main control method in malaria endemic regions has been through the use of pyrethroid-treated bed nets. Although this approach has been fairly successful, the gains are threatened by mosquito-resistance to pyrethroids, physical and chemical degradation of ITNs that reduce their efficacy, inconsistent and improper use by humans, etc. We present a model to investigate the effects of insecticide-treated bed-net use and mosquito-resistance and adaptation to pyrethroids used to treat bed nets on malaria prevalence and control in malaria endemic regions. The model captures the development and loss of resistance to insecticides, the effects of bed-net use on malaria control in a setting where proper and consistent use is not guaranteed, as well as differentiated biting of human hosts by resistant and sensitive mosquitoes. Important thresholds, including the basic reproduction number R0, and two parameter groupings that are important for disease control and for establishing the existence of endemic equilibria to the model are calculated. Furthermore, a global sensitivity analysis is carried out to identify important parameters such as insecticide treated bed-net coverage, insecticide treated bed-net efficacy, the maximum biting rate of resistant mosquitoes, etc., that drive the system and that can be targeted for disease control. Threshold levels of bed-net coverage and bed-net efficacy required for containing the disease are identified and shown to depend on the type of insecticide-resistance. For example, when mosquito-resistance to insecticides is not permanent and is acquired only through recruitment and the efficacy of insecticide-treated nets is 90%, about 70% net coverage is required to contain malaria. However, for the same insecticide-treated net efficacy, i.e., 90%, approximately 93% net coverage is required to contain the disease when resistance to insecticides is permanent and is acquired through recruitment and mutation in adult mosquitoes. The model exhibits a backward bifurcation, which implies that simply reducing R0 slightly below unity might not be enough to contain the disease. We conclude that appropriate measures to reduce or eliminate mosquito-resistance to insecticides, ensure that more people in endemic areas own and use insecticide-treated nets properly, and that the efficacy of these nets remain high most of the times, as well as educating populations in malaria endemic areas on how to keep mosquito densities low and minimize mosquito bites are important for containing malaria.