Estimation of projections to determine the extent of an endemic or epidemic in a specific population using mathematical models of the spread of infectious diseases.

Abstract

The modeling of mathematical phenomena in biology is a very useful tool to be able to easily understand the problems of reality; When analyzing disease transmission, mathematical models based on epidemiological phenomena serve to understand the mechanics of spread among members of a given population. The models that serve as the basis for this study of the dynamics of disease spread are deterministic models such as SIR, SEIR, SIS, which are the basis for obtaining more complex models.


Probabilistic methods provide powerful tools to analyze and determine the behavior of phenomena, and if their behavior is random in nature, because of this, another alternative is to study these biological phenomena using stochastic processes, or stochastic modeling.


Because the solutions to these problems cannot be obtained analytically, due to their nature, they must be solved using software and approximations of the estimates using numerical methods, these simulations will be superimposed with the simulation of the models and compare them to find trends that allow us to predict or estimate the scope of the endemics or pandemics under study and thus establish bases that allow us to apply them to different diseases, under the assumptions of each case.