Schaffer, W. M. and T. V. Bronnikova. 2009. Controlling malaria: competition, seasonality and ‘slingshotting’ transgenic mosquitoes into natural populations. Journal of Biological Dynamics. 3(2-3): 286-304.
Abstract: Forty years after the World Health Organization abandoned its eradication campaign, malaria remains a public health problem of the first magnitude with worldwide infection rates on the order of 300 million souls. The present paper reviews potential control strategies from the viewpoint of mathematical epidemiology. Following MacDonald and others, we argue in Section 1 that the use of imagicides, i.e., killing, or at least repelling, adult mosquitoes, is inherently the most effective way of combating the pandemic. In Section 2, we model competition between wild-type (WT) and plasmodium-resistant, genetically modified (GM) mosquitoes. Under the assumptions of inherent cost and prevalence-dependant benefit to transgenics, GM introduction can never eradicate malaria save by stochastic extinction of WTs. Moreover, alternative interventions that reduce prevalence have the undesirable consequence of reducing the likelihood of successful GM introduction. Section 3 considers the possibility of using seasonal fluctuations in mosquito abundance and disease prevalence to ‘slingshot’ GM mosquitoes into natural populations. By introducing GM mosquitoes when natural populations are about to expand, one can ‘piggyback’ on the yearly cycle. Importantly, this effect is only significant when transgene cost is small, in which case the non-trivial equilibrium is a focus (damped oscillations), and piggybacking is amplified by the system’s inherent tendency to oscillate. By way of contrast, when transgene cost is large, the equilibrium is a node and no such amplification is obtained.
Keywords: bifurcations, epidemiology, model, malaria, transgenic mosquitoes, mosquito, differential equation, nonlinear, system
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