This paper proposes and analyses a mathematical model for the transmission dynamics of malaria with four-time dependent control measures in Kenya: insecticide treated bed nets (ITNs), treatment, indoor residual spray (IRS), and intermittent preventive treatment of malaria in pregnancy (IPTp). We first considered constant control parameters and calculate the basic reproduction number and investigate existence and stability of equilibria as well as stability analysis. We proved that ifR0≤1, the disease-free equilibrium is globally asymptotically stable inD. IfR0>1, the unique endemic equilibrium exists and is globally asymptotically stable. The model also exhibits backward bifurcation atR0=1. IfR0>1, the model admits a unique endemic equilibrium which is globally asymptotically stable in the interior of feasible regionD. The sensitivity results showed that the most sensitive parameters are mosquito death rate and mosquito biting rates. We then consider the time-dependent control case and use Pontryagin’s Maximum Principle to derive the necessary conditions for the optimal control of the disease using the proposed model. The existence of optimal control problem is proved. Numerical simulations of the optimal control problem using a set of reasonable parameter values suggest that the optimal control strategy for malaria control in endemic areas is the combined use of treatment and IRS; for epidemic prone areas is the use of treatment and IRS; for seasonal areas is the use of treatment; and for low risk areas is the use of ITNs and treatment. Control programs that follow these strategies can effectively reduce the spread of malaria disease in different malaria transmission settings in Kenya.

Malaria remains a leading cause of mortality and morbidity among the children under five and pregnant women in sub-Saharan Africa, but it is preventable and controllable provided current recommended interventions are properly implemented. Better utilization of malaria intervention strategies will ensure the gain for the value for money and producing health improvements in the most cost effective way. The purpose of the value for money drive is to develop a better understanding (and better articulation) of costs and results so that more informed, evidence-based choices could be made. Cost effectiveness analysis is carried out to inform decision makers on how to determine where to allocate resources for malaria interventions. This study carries out cost effective analysis of one or all possible combinations of the optimal malaria control strategies (Insecticide Treated Bednets-ITNs, Treatment, Indoor Residual Spray-IRS and Intermittent Preventive Treatment for Pregnant Women-IPTp) for the four different transmission settings in order to assess the extent to which the intervention strategies are beneficial and cost effective. For the four different transmission settings in Kenya the optimal solution for the 15 strategies and their associated effectiveness are computed. Cost-effective analysis using Incremental Cost Effectiveness Ratio (ICER) was done after ranking the strategies in order of the increasing effectiveness (total infections averted). The findings shows that for the endemic regions the combination of ITNs, IRS, and IPTp was the most cost-effective of all the combined strategies developed in this study for malaria disease control and prevention; for the epidemic prone areas is the combination of the treatment and IRS; for seasonal areas is the use of ITNs plus treatment; and for the low risk areas is the use of treatment only. Malaria transmission in Kenya can be minimized through tailor-made intervention strategies for malaria control which produces health improvements in the most cost effective way for different epidemiological zones. This offers the good value for money for the public health programs and can guide in the allocation of malaria control resources for the post-2015 malaria eradication strategies and the achievement of the Sustainable Development Goals.

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