International journal of

ADVANCED AND APPLIED SCIENCES

EISSN: 2313-3724, Print ISSN:2313-626X

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 Volume 5, Issue 1 (January 2018), Pages: 123-129

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 Original Research Paper

 Title: Dynamical behavior of SIR epidemic model with non-integer time fractional derivatives: A mathematical analysis

 Author(s): Aqeel Ahmad 1, Muhammad Farman 1, *, M. O. Ahmad 1, Nauman Raza 2, M. Abdullah 3

 Affiliation(s):

 1Department of Mathematics and Statistics, University of Lahore, Lahore, Pakistan
 2Department of Mathematics, University of the Punjab Lahore, Lahore, Pakistan 
 3Department of Mathematics, University of Engineering and Technology Lahore, Lahore, Pakistan

 https://doi.org/10.21833/ijaas.2018.01.016

 Full Text - PDF          XML

 Abstract:

Protection of children from vaccine preventable diseases, such as measles is among primary goal for health worker. Measles is a highly contagious disease that can spread in a population depending on the number of peoples susceptible or infected and also depending on their dynamics in the community. The model monitors the temporal dynamics of a childhood disease in the presence of preventive vaccine. We presented a nonlinear time fractional model of measles in order to understand the outbreaks of this epidemic disease. The Caputo fractional derivative operator of order  is employed to obtain the system of fractional differential equations. The numerical solution of the time fractional model has been procured by employing Laplace Adomian decomposition method (LADM), qualitative and sensitivity analysis of the model was performed. Qualitative results shows that the model has endemic equilibrium which locally asymptotically stable for  and otherwise unstable. The convergence analysis and non-negative solutions are verified for the proposed scheme. Simulation of different epidemiological classes at the effect of fractional parameter  revealed that most individuals undergoing treatment join the recovered class. This method proves to be very efficient techniques for solving epidemic model to control infectious disease. 

 © 2017 The Authors. Published by IASE.

 This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

 Keywords: Epidemic model, Fractional derivatives, Endemic equilibrium, LADM, Convergence analysis

 Article History: Received 31 July 2017, Received in revised form 30 October 2017, Accepted 25 November 2017

 Digital Object Identifier: 

 https://doi.org/10.21833/ijaas.2018.01.016

 Citation:

 Ahmad A, Farman M, Ahmad MO, Raza N, and Abdullah M (2018). Dynamical behavior of SIR epidemic model with non-integer time fractional derivatives: A mathematical analysis. International Journal of Advanced and Applied Sciences, 5(1): 123-129

 Permanent Link:

 http://www.science-gate.com/IJAAS/2018/V5I1/Ahmad.html

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