turkmath.org

Compartmental models in epidemiology, a very general modeling technique, are applied to infectious diseases in order to determine evaluating the risk factors, suitable treatment methods, and predicting and controlling a possible outbreak. Mathematical modeling of infectious diseases with the SIR (susceptible-infected-recovered) framework was inititated in 1760 by Bernoulli [5].

In this talk, we explore that a time-scale modeling approach plays an important role to recover information from experimental data with varying domains (time scales), [6]. Mainly, we investigate the dynamics of HIV-1 (human-immunodeficiency-virus) [1], swine influenza [3], and tuberculosis [4] by proposing time-scale models which cover wide classes of models from continuous to discrete. Moreover, we demonstrate our numerical results to highlight the importance of a time-scale modeling approach.