Work

Memory-Dependent Derivative Versus Fractional Derivative (III): Difference in Modeling Epidemics

Year: 2025

Type: article

Abstract: The outbreaks of large-scale epidemics, such as COVID-19 in 2019–2022, challenge modelers. Beside the effect of the incubation period of the virus, the delay property of detection should be also stressed. This kind of memory effect affects the entire change rate, which cannot be reflected by the conventional instantaneous derivative. The fractional derivative (FD) meets this request to some extent. Yet the shortcoming of it limits its usage. Through a strict modeling approach, a new susceptible–infective–removed (SIR) model with the memory-dependent derivative (MDD) has been constructed. The numerical simulations indicate that (1) the neglecting of the incubation period may underestimate the number of susceptible individuals and overestimate the infected ones; (2) the neglecting of the treatment period may badly overestimate the removed individuals; (3) the consequence of tardy detection intervention may be very serious, and the infectious rate may increase rapidly with a postponed peak time; and (4) the SIR model with the FD yields bad estimations, not only in the primary stage but also in the subsequent evolution. Due to the reasonability of the new SIR model with the MDD, it is suggested to epidemic researchers.

Source: Fractal and Fractional

DOI: 10.3390/fractalfract9120814

Authors: Jin-Liang Wang, Hui-Feng Li

Institution: Qingdao University of Technology

Language: English

Topic: Mathematical and Theoretical Epidemiology and Ecology Models

Subfield: Public Health, Environmental and Occupational Health

Field: Medicine

Domain: Health Sciences

SDG: Good health and well-being

Open Access status: gold

Estimated APC paid: $3,258