Optimal control strategy of malaria vector using genetically modified mosquitoes

The development of transgenic mosquitoes that are resistant to diseases may provide a new and effective weapon of diseases control. Such an approach relies on transgenic mosquitoes being able to survive and compete with wild-type populations. These transgenic mosquitoes carry a specific code that inhibits the plasmodium evolution in its organism. It is said that this characteristic is hereditary and consequently the disease fades away after some time. Once transgenic mosquitoes are released, interactions between the two populations and inter-specific mating between the two types of mosquitoes take place. We present a mathematical model that considers the generation overlapping and variable environment factors. Based on this continuous model, the malaria vector control is formulated and solved as an optimal control problem, indicating how genetically modified mosquitoes should be introduced in the environment. Numerical simulations show the effectiveness of the proposed control.