Mathematical assessment of the role of vector insecticide resistance and feeding/resting behavior on malaria transmission dynamics: Optimal control analysis

Abstract

The large-scale use of insecticide-treated bednets (ITNs) and indoor residual spraying (IRS), over the last two decades, has resulted in a dramatic reduction of malaria incidence globally. However, the effectiveness of these interventions is now being threatened by numerous factors, such as resistance to insecticide in the mosquito vector and their preference to feed and rest outdoors or early in the evening (when humans are not protected by the bednets). This study presents a new deterministic model for assessing the population-level impact of mosquito insecticide resistance on malaria transmission dynamics. A notable feature of the model is that it stratifies the mosquito population in terms of type (wild or resistant to insecticides) and feeding preference (indoor or outdoor). The model is rigorously analysed to gain insight into the existence and asymptotic stability properties of the various disease-free equilibria of the model namely the trivial disease-free equilibrium, the non-trivial resistant-only boundary disease-free equilibrium and a non-trivial disease-free equlibrium where both the wild and resistant mosquito geneotypes co-exist). Simulations of the model, using data relevant to malaria transmission dynamics in Ethiopia (a malaria-endemic nation), show that the use of optimal ITNs alone, or in combination with optimal IRS, is more effective than the singular implementation of an optimal IRS-only strategy. Further, when the effect of the fitness cost of insecticide resistance with respect to fecundity (i.e., assuming a decrease in the baseline birth rate of new resistant-type adult female mosquitoes) is accounted for, numerical simulations of the model show that the combined optimal ITNs-IRS strategy could lead to the effective control of the disease, and insecticide resistance effectively managed during the first 8 years of the 15-year implementation period of the insecticides-based anti-malaria control measures in the community. Keywords: Malaria, Insecticide resistance, ITNs, IRS, Equilibria