A mathematical model is formulated based on ordinary non-linear differential equations that interprets the dynamics of dengue transmission, where the human population is divided into three compartments: susceptible persons, symptomatic persons and people, with the population of Aedes aegypti: carrier mosquitoes and non-carrier mosquitoes; simulations of the dynamic system are carried out with the MATLAB software.

A mathematical model that interprets the host-vector dynamic for a serotype of dengue is presented. The model includes four different hypotheses that consist of considering latent states in the dynamics in order to analyze the effect of these states on the basic reproduction number and changes in the evolution of the disease.

A dynamic system of nonlinear ordinary differential equations to display the infectious process of Dengue-Chikungunya, is presented. The system including a mosquito periodic mortality rate and simulations of the differential equation system by MATLAB software to determine the effect of climatic variables (temperature, humidity, pluviosity) in the infectious population mortality, is carried out.

It is formulated a stability analysis of a mathematical model to interpret the dynamics of the population growth including resistance to chemicals and phytocompounds. The threshold of the population growth of A. aegypti is determined. A sensitivity analysis and simulations of the model were developed. We conclude that the control focused in the non-resistant mosquitoes lead to a decrease in the resistant mosquitoes as well as the immature stages.

A dynamical system of non-linear ordinary differential equations which describes the Dengue-Chikungunya infectious process is reported. In this model it is considered the presence of two viruses transmitted by the same vector. Taking into account this fact, we have determined the epidemic threshold, basic reproduction number, using the next generation matrix. The simulations of the differential equations system are carried out with the MATLAB software.