Transmissão de malária baseada na dinâmica da interação entre mosquitos selvagens e transgênicos usando a genética mendeliana e a técnica de reação em cadeia mutagênica

Abstract

Recent advances in genetic manipulation have made it possible to obtain mosquitoes that are refractory to diseases, so that the transgene that blocks the cycle of the protozoan in the mosquito propagates through its descendants. The study of transgenic mosquitoes is a promising alternative for the reduction of malaria, yet disseminating genes that control a wild mosquito population has been a challenge to this day. Experiments and technological advances with the enzyme CRISPR / Cas9 through the Mutagenic Chain Reaction (MCR) technique have brought changes to this scenario. In this context, the search for mathematical models that describe the dynamics of the interaction between populations of mosquitoes living in the same geographic area has been made possible by generating simulations and experiments, verifying the behavior of populations of wild and transgenic mosquitoes. Thus, the objective of this work is to propose a mathematical model of the θ -logistic type to describe the interaction dynamics of mosquitoes, based on the dierences between classic Mendelian genetics and the MCR technique, and considering human populations in the modeling. Thus, more precise results of the implementation of the mutant gene are sought, aiming at the best methodology to reduce malaria indices with this technique. In this model the fourth-order Runge-Kutta method will be used for the approximate numerical resolution of the dierential equations used in the adopted model. The scenarios obtained from the simulations for dierent values of θ and f illustrate the pertinence of this type of system for the proposed modeling, providing guidelines on the dierences between the Mendelian genetic model and the MCR technique.