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Article

A Fractional Measles Model Having Monotonic Real Statistical Data for Constant Transmission Rate of the Disease

1
Department of Mathematics, Center for Research and Development in Mathematics and Applications (CIDMA), University of Aveiro, 3810-193 Aveiro, Portugal
2
Department of Basic Sciences and Related Studies, Mehran University of Engineering and Technology, Jamshoro 76062, Pakistan
*
Author to whom correspondence should be addressed.
Fractal Fract. 2019, 3(4), 53; https://doi.org/10.3390/fractalfract3040053
Received: 30 October 2019 / Revised: 12 November 2019 / Accepted: 18 November 2019 / Published: 21 November 2019
(This article belongs to the Special Issue 2019 Selected Papers from Fractal Fract’s Editorial Board Members)
Non-Markovian effects have a vital role in modeling the processes related with natural phenomena such as epidemiology. Various infectious diseases have long-range memory characteristics and, thus, non-local operators are one of the best choices to be used to understand the transmission dynamics of such diseases and epidemics. In this paper, we study a fractional order epidemiological model of measles. Some relevant features, such as well-posedness and stability of the underlying Cauchy problem, are considered accompanying the proofs for a locally asymptotically stable equilibrium point for basic reproduction number R 0 < 1 , which is most sensitive to the fractional order parameter and to the percentage of vaccination. We show the efficiency of the model through a real life application of the spread of the epidemic in Pakistan, comparing the fractional and classical models, while assuming constant transmission rate of the epidemic with monotonically increasing and decreasing behavior of the infected population. Secondly, the fractional Caputo type model, based upon nonlinear least squares curve fitting technique, is found to have smaller residuals when compared with the classical model. View Full-Text
Keywords: non-integer calculus; epidemiological models; numerical simulations non-integer calculus; epidemiological models; numerical simulations
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MDPI and ACS Style

Almeida, R.; Qureshi, S. A Fractional Measles Model Having Monotonic Real Statistical Data for Constant Transmission Rate of the Disease. Fractal Fract. 2019, 3, 53. https://doi.org/10.3390/fractalfract3040053

AMA Style

Almeida R, Qureshi S. A Fractional Measles Model Having Monotonic Real Statistical Data for Constant Transmission Rate of the Disease. Fractal and Fractional. 2019; 3(4):53. https://doi.org/10.3390/fractalfract3040053

Chicago/Turabian Style

Almeida, Ricardo, and Sania Qureshi. 2019. "A Fractional Measles Model Having Monotonic Real Statistical Data for Constant Transmission Rate of the Disease" Fractal and Fractional 3, no. 4: 53. https://doi.org/10.3390/fractalfract3040053

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