International journal of

ADVANCED AND APPLIED SCIENCES

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

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 Volume 6, Issue 3 (March 2019), Pages: 79-85

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 Original Research Paper

 Title: Nonstandard finite difference scheme for control of measles epidemiology

 Author(s): Farah Ashraf *, M. O. Ahmad

 Affiliation(s):

 Department of Mathematics and Statistics, University of Lahore, Lahore, Pakistan

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 * Corresponding Author. 

  Corresponding author's ORCID profile: https://orcid.org/0000-0002-5700-3822

 Digital Object Identifier: 

 https://doi.org/10.21833/ijaas.2019.03.012

 Abstract:

This paper is based on the analysis of SEIR measles models, which are used to study the integrating vaccination as a control strategy and taking the two stages of infectiousness and transmission dynamics of infectious diseases in a population. Measles is a higher contagious that can spread in a community population depending on the number of people susceptible or infected and also depending on their movement in a community. We construct an unconditionally convergent nonstandard finite difference (NSFD) scheme for SEIR measles model. NSFD preserve the positivity of all values of h. This method proved to be a very efficient technique for solving epidemic models. We obtained disease-free equilibrium (DFE) point, Endemic equilibrium (EE), reproduction number for the model. Moreover, the analysis of the epidemic models using nonstandard finite difference scheme reveals that the method provides a rapidly convergent series solution by little iteration and avoids the massive computational work. Numerical simulations show that the rate of infection is decreased with the passage of time and disease will die out in the community. The results are compared to the Differential Transformation Method to show this scheme is efficient and better accuracy for epidemic models. 

 © 2019 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: SEIR model, Qualitative analysis, DTM, NSFD, Stability analysis

 Article History: Received 26 October 2018, Received in revised form 13 January 2019, Accepted 26 January 2019

 Acknowledgement:

No Acknowledgement

 Compliance with ethical standards

 Conflict of interest:  The authors declare that they have no conflict of interest.

 Citation:

 Ashraf F and Ahmad MO (2019). Nonstandard finite difference scheme for control of measles epidemiology. International Journal of Advanced and Applied Sciences, 6(3): 79-85

 Permanent Link to this page

 Figures

 Fig. 1 Fig. 2 Fig. 3 Fig. 4 Fig. 5 Fig. 6 Fig. 7 Fig. 8 Fig. 9 Fig. 10 Fig. 11 Fig. 12 Fig. 13 

 Tables

 Table 1 Table 2 

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