Fractional <i>SIS</i> Epidemic Models

• Main Authors: Caterina Balzotti, Mirko D’Ovidio, Paola Loreti
• Format: Article
• Language: English
• Published: MDPI AG 2020-08-01
• Series: Fractal and Fractional
• Subjects: α-SIS model; SIS model; epidemic models; fractional logistic equation
• Online Access: https://www.mdpi.com/2504-3110/4/3/44

In this paper, we consider the fractional <inline-formula><math display="inline"><semantics><mrow><mi>S</mi><mi>I</mi><mi>S</mi></mrow></semantics></math></inline-formula> (susceptible-infectious-susceptible) epidemic model (<inline-formula><math display="inline"><semantics><mi>α</mi></semantics></math></inline-formula>-<inline-formula><math display="inline"><semantics><mrow><mi>S</mi><mi>I</mi><mi>S</mi></mrow></semantics></math></inline-formula> model) in the case of constant population size. We provide a representation of the explicit solution to the fractional model and we illustrate the results by numerical schemes. A comparison with the limit case when the fractional order <inline-formula><math display="inline"><semantics><mi>α</mi></semantics></math></inline-formula> converges to 1 (the <inline-formula><math display="inline"><semantics><mrow><mi>S</mi><mi>I</mi><mi>S</mi></mrow></semantics></math></inline-formula> model) is also given. We analyze the effects of the fractional derivatives by comparing the <inline-formula><math display="inline"><semantics><mrow><mi>S</mi><mi>I</mi><mi>S</mi></mrow></semantics></math></inline-formula> and the <inline-formula><math display="inline"><semantics><mi>α</mi></semantics></math></inline-formula>-<inline-formula><math display="inline"><semantics><mrow><mi>S</mi><mi>I</mi><mi>S</mi></mrow></semantics></math></inline-formula> models.