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Effects of Fractional Derivatives with Different Orders in SIS Epidemic Models

by 1,†, 2,†, 2,*,† and 2,†
1
Istituto per le Applicazioni del Calcolo, Consiglio Nazionale delle Ricerche, 00185 Rome, Italy
2
Dipartimento di Scienze di Base e Applicate per l’Ingegneria, Sapienza Università di Roma, 00161 Rome, Italy
*
Author to whom correspondence should be addressed.
These authors contributed equally to this work.
Academic Editor: Ravi P. Agarwal
Computation 2021, 9(8), 89; https://doi.org/10.3390/computation9080089
Received: 15 July 2021 / Revised: 3 August 2021 / Accepted: 4 August 2021 / Published: 8 August 2021
(This article belongs to the Section Computational Biology)
We study epidemic Susceptible–Infected–Susceptible (SIS) models in the fractional setting. The novelty is to consider models in which the susceptible and infected populations evolve according to different fractional orders. We study a model based on the Caputo derivative, for which we establish existence results of the solutions. Furthermore, we investigate a model based on the Caputo–Fabrizio operator, for which we provide existence of solutions and a study of the equilibria. Both models can be framed in the context of SIS models with time-varying total population, in which the competition between birth and death rates is macroscopically described by the fractional orders of the derivatives. Numerical simulations for both models and a direct numerical comparison are also provided. View Full-Text
Keywords: Caputo derivative; Caputo–Fabrizio operator; Susceptible–Infected–Susceptible (SIS) models Caputo derivative; Caputo–Fabrizio operator; Susceptible–Infected–Susceptible (SIS) models
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MDPI and ACS Style

Balzotti, C.; D’Ovidio, M.; Lai, A.C.; Loreti, P. Effects of Fractional Derivatives with Different Orders in SIS Epidemic Models. Computation 2021, 9, 89. https://doi.org/10.3390/computation9080089

AMA Style

Balzotti C, D’Ovidio M, Lai AC, Loreti P. Effects of Fractional Derivatives with Different Orders in SIS Epidemic Models. Computation. 2021; 9(8):89. https://doi.org/10.3390/computation9080089

Chicago/Turabian Style

Balzotti, Caterina, Mirko D’Ovidio, Anna C. Lai, and Paola Loreti. 2021. "Effects of Fractional Derivatives with Different Orders in SIS Epidemic Models" Computation 9, no. 8: 89. https://doi.org/10.3390/computation9080089

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