Malaria has been a preeminent threat in the lives of millions throughout the world. The global fight against malaria has been on-going for several decades and has called for the usage of mathematics tools to help curb the spread of the disease. Controls representing malaria intervention methods were added to an SEIR-SEI compartmental model. We found an analytic form for the basic reproductive number and the disease-free equilibrium. We used the Jacobian of the model to check the stability of the modelâs equilibrium points. The model was analyzed to determine the effect that controls and parameter values have on the basic reproductive number. We discretized the compartmental model and used the equations as part of the constraint set for a nonlinear programming model designed to report the optimal distribution of malaria intervention methods. We considered two objective functions for the nonlinear programming problem, one based on the infected human population, and one based on the infected mosquito population, with the goal of minimizing these objectives with respect to the control variables. We solve the nonlinear programming model to find the optimal intervention plan for every combination of budget and objective function. The optimization model considers two districts with different human and mosquito populations. The districts share a budget, used to fund their intervention methods. The optimal intervention plans found by the model show the usage rate of each intervention method in each time period, for both districts. A hierarchy of intervention methods is revealed for each district. We found that the portion of the budget spent in each district depends on the objective being considered and the difference in population for each district. When the budget is smaller, the resulting optimal intervention plan reports the same hierarchy of intervention methods. When the budget is larger, the optimization plan expands usage of interventions in an expected fashion. The infected human and mosquito populations decrease when the optimal intervention plan is used in each scenario. The intervention plans found by the optimization model minimize the infected mosquito and human populations and accomplish the goal of minimizing the burden of malaria on the two-district society we considered. We first extend the optimization model to so that interventions last for multiple time periods. We compare the results of this model to the results generated by the previous model with singleperiod interventions. We then extend the multiple-period model to consider visitation between the two districts. The visitation model involves a two-district compartmental model with parameters representing visitation connecting what otherwise would be two instances of our single district compartmental model. We repeat the analysis of the single district compartmental model for the two-district compartmental model.
