TY - JOUR
T1 - On a Novel Dynamics of SEIR Epidemic Models with a Potential Application to COVID-19
AU - Rangasamy, Maheswari
AU - Chesneau, Christophe
AU - Martin-Barreiro, Carlos
AU - Leiva, Víctor
N1 - Funding Information:
This research was supported partially funded by FONDECYT grant number 1200525 (V.L.) from the National Agency for Research and Development (ANID) of the Chilean government under the Ministry of Science, Technology, Knowledge, and Innovation.
Publisher Copyright:
© 2022 by the authors.
PY - 2022/7
Y1 - 2022/7
N2 - In this paper, we study a type of disease that unknowingly spreads for a long time, but by default, spreads only to a minimal population. This disease is not usually fatal and often goes unnoticed. We propose and derive a novel epidemic mathematical model to describe such a disease, utilizing a fractional differential system under the Atangana–Baleanu–Caputo derivative. This model deals with the transmission between susceptible, exposed, infected, and recovered classes. After formulating the model, equilibrium points as well as stability and feasibility analyses are stated. Then, we present results concerning the existence of positivity in the solutions and a sensitivity analysis. Consequently, computational experiments are conducted and discussed via proper criteria. From our experimental results, we find that the loss and regain of immunity result in the gain and loss of infections. Epidemic models can be linked to symmetry and asymmetry from distinct points of view. By using our novel approach, much research may be expected in epidemiology and other areas, particularly concerning COVID-19, to state how immunity develops after being infected by this virus.
AB - In this paper, we study a type of disease that unknowingly spreads for a long time, but by default, spreads only to a minimal population. This disease is not usually fatal and often goes unnoticed. We propose and derive a novel epidemic mathematical model to describe such a disease, utilizing a fractional differential system under the Atangana–Baleanu–Caputo derivative. This model deals with the transmission between susceptible, exposed, infected, and recovered classes. After formulating the model, equilibrium points as well as stability and feasibility analyses are stated. Then, we present results concerning the existence of positivity in the solutions and a sensitivity analysis. Consequently, computational experiments are conducted and discussed via proper criteria. From our experimental results, we find that the loss and regain of immunity result in the gain and loss of infections. Epidemic models can be linked to symmetry and asymmetry from distinct points of view. By using our novel approach, much research may be expected in epidemiology and other areas, particularly concerning COVID-19, to state how immunity develops after being infected by this virus.
KW - ABC derivatives
KW - basic reproduction number
KW - equilibrium points
KW - fractional derivatives
KW - Laplace transform
KW - numerical methods
KW - SARS-CoV-2
KW - sensitivity and stability analyses
UR - http://www.scopus.com/inward/record.url?scp=85137253815&partnerID=8YFLogxK
U2 - 10.3390/sym14071436
DO - 10.3390/sym14071436
M3 - Article
AN - SCOPUS:85137253815
VL - 14
JO - Symmetry
JF - Symmetry
SN - 2073-8994
IS - 7
M1 - 1436
ER -