A Mathematical Model for Aedes egypti Dispersal References
A Mathematical Model for Aedes egypti. Dispersal. W.C. Ferreira Jr.1 , N .Maidana2 and Lucy Takahashi3. Dengue is a very serious virotic disease transmitted ...
A Mathematical Model for Aedes egypti Dispersal W.C. Ferreira Jr.1 , N .Maidana2 and Lucy Takahashi3 . Dengue is a very serious virotic disease transmitted by the Aedes egypti mosquito which spreads throughout tropical Americas. Since no effective vaccine against dengue is predicted for the near future, the only possible way to lower its impact on human populations is by controlling the proliferation and dispersal of the vector population. This work proposes a non linear mathematical model for the Aedes egypti dynamics which takes into account its larvae and airborne forms as two coupled subpopulations. The airborne population spread by (wind blowing) transport and (self) diffusion while the larvae dynamics is static, grows by oviposition and decreases due to its development into mosquitoes and natural death. Numerical simulations show that a stable front wave invasion develops quickly from any sufficiently strong initial perturbation. A mathematical analysis gives the conditions for the existence of travelling waves and the wave speed dependence on crucial parameters is plotted. A biological interpretation of the results indicates possible strategies for stopping the front wave propagation by an appropriate modification of the medium with respect to mosquito vital dynamics.
References [1] J.D.Murray, Mathematical Biology, Springer-Verlag, New York 1993. [2] N.Shigesada, K.Kawasaki, Biological Invasions: Theory and Practice, Oxford University Press, New York 1997 1
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