Stability of Solutions in a Population Model with Transgenic Mosquitoes

Start: 02/20/2013 - 4:15pm
End  : 02/20/2013 - 5:15pm


Hubertus Von Bremen, Cal Poly Pomona


Mosquitoes transmit many fatal and debilitating diseases such as malaria, dengue, West Nile virus and many more. One possible way to reduce the transmission of mosquito- borne diseases is to release, in the wild, genetically altered mosquitoes that can no longer transmit a given disease. These altered mosquitoes would interact with the wild mosquitoes and reproduce. Recent research has shown that it is technically possible to genetically alter mosquitoes in such a way that they can no longer transmit certain parasites. An extension of a discrete-time population dynamics model by Jia Li for wild and genetically altered mosquitoes that takes into account the effect of seasonal variability is presented. The seasonal variability is introduced into the model by allowing the birth and survival functions to have periodic parameters. We consider the stability of periodic solutions of the ratio dynamics and show that under certain conditions the ratios converge to an attracting periodic state that depends only on the birth functions and not the survival probabilities. Using the ratio dynamics we decouple the system into two Ricker equations with periodic parameters. The stability of the periodic solutions of the original system is given by the stability of the uncoupled system.

Beckman B126, Harvey Mudd College

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