An approach to population-based epidemiologic models

Abstract

Introduction: Mathematical biology or biomathematics is a scientific area that studies and models biological processes with the use of mathematical techniques and methods. It is of great importance in the formulation of mathematical models that describe the dynamics of processes associated with biological and medical phenomena and especially for epidemiology in its purpose of characterizing the clinical and social context in the dynamics of contagious diseases.

Objective: To argue the different forms of population epidemiological models essential in the treatment and management of communicable diseases and epidemics, through a relatively diverse bibliographic search.

Development: Starting from the classical Kermack-McKendrick formulation, we present an overview of the models defined by ordinary differential equations for their proven performance in the mathematical description of the spread of diseases. In a second moment, we present within the probabilistic models, the so-called urn models, which allow another approach, equally valid but of more recent use.

Conclusions: Biomathematics is a multidisciplinary science in constant development and therefore, the models presented in this study are only an approach to two different approaches from the mathematical point of view, such as the population models defined by ordinary differential equations and commonly solved by numerical and computational analysis techniques and the probabilistic urn models.

Keywords: biomathematics; epidemiological models; ordinary differential equations; urns.