Mathematical Models of the spread and prevention of infectious diseases.

In the first part of this talk we show some estimates on the arrival times of the first infectious peak (outbreak) of Covid 19 in Mexico. These estimates were made with the Epidemiological Emergency Group for Covid_19 at UNAM in Mexico and they turned out to be quite accurate. Later we will show more recent work on some ways to use vaccination not only to prevent deaths and hospitalizations but also to stop an infectious front or mitigate its geographic transmission.

The mathematical models that we present in this talk consist mainly of classical epidemiology models such as Kermack and McKendrick coupled with continuous diffusion or discrete diffusion on a graph. Also, in some cases the coefficients are variables to simulate a changing environment. The idea is to achieve a sufficiently precise model to obtain useful and precise estimates, but also to keep the model manageable enough to properly estimate the necessary parameters which are usually not estimated a priori, especially when dealing with a new infection such as Covid-19.