Mathematics of an epidemiology-genetics model for assessing the role of insecticides resistance on malaria transmission dynamics

Although the widespread use of indoors residual spraying (IRS)and insecticides treated bednets (ITNs; later replaced by long-lasting insecticidal nets (LLINs))has led to a dramatic reduction of malaria burden in endemic areas, such usage has also resulted in the major challenge of the evolution of insecticide resistance in the mosquito population in those areas. Thus, efforts to combat malaria also include the urgent problem of effectively managing insecticide resistance. This study is based on the design and analysis of a new mathematical model for assessing the impact of insecticides resistance in the mosquito population (due to widespread use of IRS and ITNs)on the transmission dynamics and control of malaria in a community. The model, which couples disease epidemiology with vector population genetics, incorporates several fitness costs associated with insecticide resistance. Detailed rigorous analysis of the model is presented. Using data and parameter values relevant to malaria dynamics in moderate and high malaria transmission settings in some parts of Ethiopia, simulations of the model show that, while the ITNs-IRS strategy can lead to the effective control of the disease in both the moderate and high malaria transmission setting if the ITNs coverage level in the community is high enough (regardless of the level of IRS coverage), it fails to manage insecticide resistance (as measured in terms of the frequency of resistant allele at equilibrium in the community). It is further shown that the effective size of the coverage level of the ITNs and IRS required to effectively control the disease, while effectively managing insecticide resistance in the mosquito population, depends on the magnitude of the level of resistant allele dominance (in mosquitoes with heterozygous genotype)and several fitness costs associated with the insecticide resistance in the vector population. For instance, in a moderate transmission setting, malaria burden can be reduced to low levels of endemicity (even with low coverage of ITNs and IRS), and insecticide resistance effectively managed, if the fitness costs of resistance are at their assumed baseline values. Such reduction is not achievable if the fitness costs of resistance are lower than the baseline values.