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Behaviors and numerical simulations of malaria dynamic models with transgenic mosquitoes. (English) Zbl 1406.92596

Summary: The release of transgenic mosquitoes to interact with wild ones is a promising method for controlling malaria. How to effectively release transgenic mosquitoes to prevent malaria is always a concern for researchers. This paper investigates two methods of releasing transgenic mosquitoes and proposes two epidemic models involving malaria patients, anopheles, wild mosquitoes, and transgenic mosquitoes based on system of continuous differential equations. A basic reproduction number \(\mathbf{R}_0\) is defined for the models and it serves as a threshold parameter that predicts whether malaria will spread. By theoretical analysis of the dynamic behaviors of the models and numerical simulations, it is verified that malaria can be effectively controlled by the opportune release of transgenic mosquitoes; that is, when \(\mathbf{R}_0 \leq 1\), malaria will disappear; when \(\mathbf{R}_0 > 1\), malaria will become an endemic disease in the target field.

MSC:

92D30 Epidemiology
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