Abstract
In this paper, we consider the fractional SIS (susceptible-infectious-susceptible) epidemic model (α-SIS 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 α converges to 1 (the SIS model) is also given. We analyze the effects of the fractional derivatives by comparing the SIS and the α-SIS models.
Highlights
The study of mathematical models for epidemiology has a long history, dating back to the early 1900s with the theory developed by Kermack and McKendrick [1]
The use of mathematical models for epidemiology is useful to predict the progress of an infection and to take strategy to limit the spread of the disease
In order to compute the solution to the fractional SIS model for any set of parameters and any initial datum, we propose and compare two numerical schemes to approximate (1)
Summary
The study of mathematical models for epidemiology has a long history, dating back to the early 1900s with the theory developed by Kermack and McKendrick [1]. Such theory describes compartmental models, where the population is divided into groups depending on the state of individuals with respect to disease, distinguishing between groups. The SIS model has a long history, too [2] It describes the spread of human viruses, such as influenza. SIS is a model without immunity, where the individual recovered from the infection comes back into the class of susceptibles
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