Applied Mathematics, 2016, 7, 542-555 Published Online March 2016 in SciRes. http://www.scirp.org/journal/am http://dx.doi.org/10.4236/am.2016.76050 How to cite this paper: Wairimu, J. and Ronoh, M. (2016) Modeling Insecticide Resistance in Endemic Regions of Kenya. Applied Mathematics, 7, 542-555. http://dx.doi.org/10.4236/am.2016.76050 Modeling Insecticide Resistance in Endemic Regions of Kenya Josephine Wairimu, Marilyn Ronoh School of Mathematics, University of Nairobi, Nairobi, Kenya Received 30 November 2015; accepted 27 March 2016; published 30 March 2016 Copyright © 2016 by authors and Scientific Research Publishing Inc. This work is licensed under the Creative Commons Attribution International License (CC BY). http://creativecommons.org/licenses/by/4.0/ Abstract In this study, we develop an SIS model for two types of mosquitoes, a traditional one and one that is resistant to IRS and ITNs. The resistant mosquito develops behavioral adaptation to control measures put in place to reduce their biting rate. They also bite early before dusk and later after dark when people are outside the houses and nets. We determine the effect of the two types of mosquitoes on malaria transmission in Kenya. The basic reproduction number 0  is established as a sharp threshold that determines whether the disease dies out or persists in the population. Precisely, if 0  ≤ 1, the disease-free equilibrium is globally asymptotically stable and the disease always dies out and if 0  > 1, there exists a unique endemic equilibrium which is globally stable and the disease persists. The contribution of the two types of mosquitoes to the basic reproduc- tion number and to the level of the endemic equilibrium is analyzed. Keywords Malaria, Insecticide Resistance, ITNs, IRS, Reproduction Number 1. Introduction Malaria is one of the leading causes of morbidity and mortality in Kenya and it kills an estimated 34,000 child- ren under five every year. Economically, it is estimated that 170 million working days in Kenya are lost each year because of malaria illness. http://kenya.usaid.gov/programs/health/72 . After 1990, pyrethroids were promoted as insecticides of choice especially for Insecticides Treated Nets (ITNs) and Indoor Residual Spray (IRS) [1] [2], due to high efficacy, rapid rate of knockdown, strong mosquito excito-repellence and low mammalian toxicity [3]. In Kenya, ITNs have mainly been distributed to pregnant women and children under 5 years old by the Kenya