Numerical method for simulating the model of using insecticide for the optimal control of mosquitoes for the eradication of malaria

In order to simulate the mathematical model of eliminating malaria by controlling the population of mosquitoes with insecticide and the insecticide's residual effects, the study developed a four points hybrid block algorithm. The convergence and stability qualities of the block method are established. The block approach is applied after the variable control problems are generated using Pontryagin's principle. The forward-backward sweep methods of the block method are applied. The method is then implemented using a computer code using MATLAB R2018a mathematical software. According to the findings of this study, the simulated result from this approach displayed a significantly lower number of mosquitoes while lessening the negative effects of the insecticide, which in turn will reduce the high rate of malaria spreading.