Applied Mathematics & Information Sciences

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We present a system of ordinary nonlinear differential equations describing the population growth dynamics of the Aedes aegypti mosquito, the main transmitter of the dengue virus in Colombia. This model incorporates the three types of known control for mosquito eradication: mechanical, biological and chemical, focusing on biological control through the use of the Wolbachia bacterium, which is the new hope for the control of the diseases transmitted by this mosquito. A local stability analysis of the model is performed on the three equilibrium points that are found, determining the conditions under which those points become stable or unstable. Finally, we present numerical simulations implemented in Matlab, where the numerical results are obtained using hypothetical values of the parameters obtained from the literature.

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