The significance of the latent period in the mathematical modeling of airborne diseases

Although the latent phase affects disease transmission on a population scale, this stage is not easy to detect and trace. In this study, the explanation of latent period with classical (SEIR) and delayed compartment-based mathematical models are presented comparatively. Mathematical analyses of these models are carried out and their advantages and disadvantages are discussed. Additionally, parameter estimations and computational simulations are performed by using the data of three airborne diseases from various regions, namely, COVID-19 Omicron variant (USA, India, Brazil), Influenza A H1N1 (Mexico, USA, England), and meningococcal meningitis (South Africa, USA, Australia). The findings demonstrate that, for a specific value of delay, the delayed SEIR model exhibits a lower reproduction number and a lower peak value compared to the standard SEIR model. This suggests that the delayed SEIR model may be particularly suitable for scenarios characterized by delayed disease transmission dynamics, such as diseases with longer incubation periods or significant asymptomatic periods. The results provide insight into the applicability of the delayed SEIR model and its advantages over the standard SEIR model in specific epidemiological scenarios.