Optimal Releases for Population Replacement Strategies: Application to Wolbachia

In this article, we consider a simplified model of time dynamics for a mosquito population subject to the artificial introduction of Wolbachia-infected mosquitoes in order to fight arboviruses tran...

[1]  Karyn N. Johnson,et al.  Solving the Wolbachia Paradox: Modeling the Tripartite Interaction between Host, Wolbachia, and a Natural Enemy , 2011, The American Naturalist.

[2]  Ernst Hairer,et al.  Error of Runge-Kutta methods for stiff problems studied via differential algebraic equations , 1988 .

[3]  Hernán G. Solari,et al.  A Stochastic Spatial Dynamical Model for Aedes Aegypti , 2008, Bulletin of mathematical biology.

[4]  T. Adak,et al.  Population replacement in Culex fatigens by means of cytoplasmic incompatibility. Laboratory experiments with non-overlapping generations. , 1974, Bulletin of the World Health Organization.

[5]  Martin Strugarek,et al.  Reduction to a Single Closed Equation for 2-by-2 Reaction-Diffusion Systems of Lotka-Volterra Type , 2016, SIAM J. Appl. Math..

[6]  Olga Vasilieva,et al.  Establishing wMelPop Wolbachia Infection among Wild Aedes aegypti Females by Optimal Control Approach , 2017 .

[7]  Erik J. Balder.  On equivalence of strong and weak convergence inL1-spaces under extreme point conditions , 1991 .

[8]  E. Zuazua,et al.  Allee optimal control of a system in ecology , 2018, Mathematical Models and Methods in Applied Sciences.

[9]  J. Penot,et al.  Tangent sets to unilateral convex sets , 1995 .

[10]  J. Lei.  Monotone Dynamical Systems , 2013 .

[11]  Olga Vasilieva,et al.  Optimal control approach for establishing wMelPop Wolbachia infection among wild Aedes aegypti populations , 2018, Journal of mathematical biology.

[12]  Cécile Carrère,et al.  Optimization of an in vitro chemotherapy to avoid resistant tumours. , 2017, Journal of theoretical biology.

[13]  Peter S Kim,et al.  Modelling a Wolbachia Invasion Using a Slow–Fast Dispersal Reaction–Diffusion Approach , 2013, Bulletin of mathematical biology.

[14]  N. Barton,et al.  Spatial Waves of Advance with Bistable Dynamics: Cytoplasmic and Genetic Analogues of Allee Effects , 2011, The American Naturalist.

[15]  Ernst Caspari,et al.  ON THE EVOLUTIONARY IMPORTANCE OF CYTOPLASMIC STERILITY IN MOSQUITOES , 1959 .

[16]  M Hertig,et al.  Studies on Rickettsia-Like Micro-Organisms in Insects. , 1924, The Journal of medical research.

[17]  Lorenz T. Biegler,et al.  On the implementation of an interior-point filter line-search algorithm for large-scale nonlinear programming , 2006, Math. Program..

[18]  Brian W. Kernighan,et al.  AMPL: A Modeling Language for Mathematical Programming , 1993 .

[19]  S. Ritchie,et al.  Successful establishment of Wolbachia in Aedes populations to suppress dengue transmission , 2011, Nature.

[20]  Jimmy Lamboley,et al.  Properties of optimizers of the principal eigenvalue with indefinite weight and Robin conditions , 2016, 1605.06400.

[21]  Peter Hinow,et al.  Structured and Unstructured Continuous Models for Wolbachia Infections , 2009, Bulletin of mathematical biology.

[22]  Joshua G Schraiber,et al.  Constraints on the use of lifespan-shortening Wolbachia to control dengue fever. , 2012, Journal of theoretical biology.

[23]  M. Laird,et al.  Eradication of Culex pipiens fatigans through Cytoplasmic Incompatibility , 1967, Nature.

[24]  H. Yang,et al.  Optimal control of Aedes aegypti mosquitoes by the sterile insect technique and insecticide. , 2010, Mathematical biosciences.

[25]  R. Maciel-de-Freitas,et al.  From Lab to Field: The Influence of Urban Landscapes on the Invasive Potential of Wolbachia in Brazilian Aedes aegypti Mosquitoes , 2015, PLoS neglected tropical diseases.

[26]  J. Werren,et al.  Wolbachia: master manipulators of invertebrate biology , 2008, Nature Reviews Microbiology.

[27]  N. F. Britton,et al.  Modelling the Use of Wolbachia to Control Dengue Fever Transmission , 2013, Bulletin of mathematical biology.

[28]  Jorge Hendrichs,et al.  Back to the future: the sterile insect technique against mosquito disease vectors. , 2015, Current opinion in insect science.

[29]  S. Ritchie,et al.  The wMel Wolbachia strain blocks dengue and invades caged Aedes aegypti populations , 2011, Nature.

[30]  Antoine Henrot,et al.  Variation et optimisation de formes , 2005 .