Insecticide-resistant mosquitoes and malaria control

• Global stability of disease and insecticide free fixed point is proved.
• High mosquito density plus insecticide resistance challenges malaria control.
• If mutation is low, reduce mosquito below a critical level to control malaria.
• Proper personal protection reduces malaria prevalence even if there is resistance.
• Increased insecticide resistance rate in mosquito challenges malaria control.

The emergence of insecticide-resistant mosquitoes strongly challenges the fight against mosquito-borne diseases, in particular malaria. In this paper, we formulate a system of nonlinear difference equations for malaria transmission cycle. Our model incorporates compartments for insecticide-resistant mosquitoes, where mutation is the only evolutionary force involved in the occurrence of resistant allele in the mosquito population. By deriving an epidemiological threshold, the global stability of the disease and the resistance-free fixed point is established for reduced recruitment rates of resistant mosquitoes. Furthermore, by employing numerical techniques, we showed that the mosquito–human transmission cycle of malaria and its prevalence could be impacted by mutation rate, the personal protection of hosts and the density of mosquitoes. Our results highlight that given a large mosquito population, the presence of even a small number of resistant mosquitoes to an insecticide could make the insecticide ineffective for malaria control. This suggests the need for effective insecticide management strategy, alternate mosquito control approaches, educating the public about personal protection and reduction of mosquito population in a given environment.