Mathematical Modeling of the Infectious Diseases: Key Concepts and Applications

Abstract

Background:The transmission dynamics of infectious diseases is susceptible to changes governed by several factors, whose recognition is critical for the rational development of strategies for prevention and control, as well as for developing health policies. In this context, mathematical modeling can provide useful insights concerning transmission patterns and detection of parameters to mitigate disease in the population.Objectives: To didactically present the mathematical modeling of infectious diseases for health students and professionals as a tool in epidemiology.Methods: A comprehensive literature review was conducted with articles obtained from PubMed, Web of Science, and Google Scholar databases with the term infectious diseases mathematical modeling.Results: There are two main types of models built with a basis on fixed or probabilistic rates that describe individuals' movement in compartments that designate stages in the natural history of the disease. In this sense, deterministic models are non-probabilistic and stochastic models are probabilistic, the first one helps in developing a prospection of possible scenarios in epidemiology, while the second is more applicable in the study of the influence of variables in the transmission dynamics. Conclusion:The infectious agents are in a constant process of biological evolution, as well as the environment and human conceptions, culture, and behavior, implying a constant transformation in the epidemiological profile of infectious diseases, in which the mathematical modeling can provide support to the decision-making processes concerning epidemiology and public health.