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Occurrence of Bifurcations in epidemiological models: significance in the prediction of disease transmission
This paper presents the state of the art on the study of the occurrence of different types of bifurcations and their implications in different compartmental epidemiological models applied to different infectious diseases. Emphasis is placed on investigating how deeply the occurrence of the backward bifurcation and the Hopf bifurcation have been studied, the latter being the cause of the appearance of oscillatory patterns in the number of infected individuals. The application of mathematical models is a reliable tool to describe the dynamics of epidemics and for the formulation of public policies that minimize the incidence of the disease or that contribute to its eradication. The transmission of infectious diseases is a very complex phenomenon that involves dissimilar factors and parameters and not all diseases have the same development, so there are different models. Among the most used are the compartmental models that range from the simplest, which only consider two compartments, susceptible population and infected population (SI) to other very complex ones that can also consider exposed, recovered, vaccinated, quarantined population, among others. Some studies have shown that the dynamics of these models is determined by the basic reproduction number of the disease R0, generally considering that the disease can be eradicated if R0<1. However, other investigations have shown that this criterion is not always sufficient to control the spread of the disease, as a phenomenon known as backward bifurcation appears. Hence the importance attached to the study and qualitative analysis of epidemiological models.
