Study of Bacterial Growth Population Dynamics in Laboratory Using Interval Differential Equations - Barelli, Vitor Eduardo Girotto; Wasques, Vinícius Francisco; Smetana, Juliana Helena Costa; Loss, Ana Luiza Poletto; Ribeiro, Gabriel Viégas (C.Q.D. - Revista Eletrônica Paulista de Matemática, 2025)
This work focused on studying the population dynamics of Escherichia coli growth in a laboratory setting using Interval Differential Equations (IDEs). Specifically, the Malthus and Verhulst models were considered to describe population growth dynamics, using parameters collected from laboratory experiments. These parameters, as reported in the article, have an interval-valued characteristic. Supported by analytical and numerical methods—Euler and fourth-order Runge-Kutta, modified for the interval theory context—interval numerical solutions were produced to study these models. The work demonstrated that IDEs, particularly the Verhulst model, faithfully represent biological data due to the intrinsic uncertainties of the system.
Keywords: Interval Differential Equations; Malthus Model; Verhulst Model; Escherichia coli; Euler Method; Runge-Kutta Method