Analytical and Numerical Boundedness of a Model with Memory Effects for the Spreading of Infectious Diseases
Zafar Iqbala, Jorge E. Macías‐Díazb c✉, Nauman Ahmeda, Aqsa Javaida, Muhammad Rafiqd e, Ali Razaf
- aDepartment of Mathematics and Statistics, The University of Lahore, Lahore 54590, Pakistan
- bDepartamento de Matemáticas y Física, Universidad Autónoma de Aguascalientes, Aguascalientes 20100, Mexico
- cDepartment of Mathematics and Didactics of Mathematics, Tallinn University, 10120 Tallinn, Estonia
- dDepartment of Mathematics, Faculty of Science and Technology, University of Central Punjab, Lahore 54590, Pakistan
- eMathematics Research Center, Department of Mathematics, Near East University, Near East Boulevard, Mersin 10, Nicosia 99138, Turkey
- fDepartment of Mathematics, Government of Mulana Zafar Ali Khan Graduate College Wazirabad, Lahore 54000, Pakistan
- ✉Corresponding author
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Abstract
In this study, an integer-order rabies model is converted into the fractional-order epidemic model. To this end, the Caputo fractional-order derivatives are plugged in place of the classical derivatives. The positivity and boundedness of the fractional-order mathematical model is investigated by applying Laplace transformation and its inversion. To study the qualitative behavior of the non-integer rabies model, two steady states and the basic reproductive number of the underlying model are worked out. The local and global stability is investigated at both the steady states of the fractional-order epidemic model. After analytic treatment, a structure-preserving numerical template is constructed to numerically solve the fractional-order epidemic model. Moreover, the positivity, boundedness and symmetry of the numerical scheme are examined. Lastly, numerical experiment and simulations are accomplished to substantiate the significant traits of the projected numerical design. Consequences of the study are highlighted in the closing section.
TL;DRThe Caputo fractional-order derivatives are plugged in place of the classical derivatives to study the qualitative behavior of the non-integer rabies model and to substantiate the significant traits of the projected numerical design. (Semantic Scholar)