Mexican mathematics and its fight against Dengue: Achievements and challenges

In this work, we made a review of some of the mathematical models that have been used by mexican mathematicians to model and simulate the spread of Dengue. Either deterministic, empirical, or statistical analysis models are discussed.  Posing in some cases control measures to reduce or prevent the spread of dengue. Both deterministic models or statistical analyzes are reviewed: methodologies that involve analysis, modeling and simulation, successful cases of their applications for the calculation of specific quantities and of importance for health experts are listed and classified as the basic reproduction number or the risk of contagion analysis. Reflections of the challenges and future implications that should be included in the mathematical models to simulate the prevention and control of the spread of dengue in Mexico are also included.Some of the extensions that have been made to the traditional models and the added variables are listed, successful cases of their applications for the calculation of specific important quantities for health experts such as: the basic reproduction number or the risk analysis of infection. Reflections of the challenges and future modifications that should be included in the models to simulate Dengue spread are included.