Open Access

ARTICLE

Computational Investigation of Hand Foot Mouth Disease Dynamics with Fuzziness

by Dumitru Baleanu^1,2,3, Fazal Dayan⁴, Nauman Ahmed^3,5,*, Muhammad Rafiq^6,7, Ali Raza^3,8, Muhammad Ozair Ahmad⁵

1 Department of Mathematics, Cankaya University, Balgat, Ankara, 06530, Turkey
2 Department of Medical Research, China Medical University, Taichung, 406040, Taiwan
3 Department of Computer Science and Mathematics, Lebanese American University, Beirut, Lebanon
4 Department of Mathematics, School of Science, University of Management and Technology, Lahore, 54000, Pakistan
5 Department of Mathematics and Statistics, University of Lahore, Lahore, 54590, Pakistan
6 Department of Mathematics, Faculty of Science and Technology, University of Central Punjab, Lahore, 54000, Pakistan
7 Near East University, Mathematics Research Center, Department of Mathematics, Near East Boulevard, 99138, Nicosia/Mersin 10, Turkey
8 Department of Mathematics, Govt. Maulana Zafar Ali Khan Graduate College Wazirabad, Punjab Higher Education Department (PHED), Lahore, 54000, Pakistan

* Corresponding Author: Nauman Ahmed. Email:

Computers, Materials & Continua 2023, 75(2), 4175-4189. https://doi.org/10.32604/cmc.2023.034868

Received 30 June 2022; Accepted 26 January 2023; Issue published 31 March 2023

Abstract

The first major outbreak of the severely complicated hand, foot and mouth disease (HFMD), primarily caused by enterovirus 71, was reported in Taiwan in 1998. HFMD surveillance is needed to assess the spread of HFMD. The parameters we use in mathematical models are usually classical mathematical parameters, called crisp parameters, which are taken for granted. But any biological or physical phenomenon is best explained by uncertainty. To represent a realistic situation in any mathematical model, fuzzy parameters can be very useful. Many articles have been published on how to control and prevent HFMD from the perspective of public health and statistical modeling. However, few works use fuzzy theory in building models to simulate HFMD dynamics. In this context, we examined an HFMD model with fuzzy parameters. A Non Standard Finite Difference (NSFD) scheme is developed to solve the model. The developed technique retains essential properties such as positivity and dynamic consistency. Numerical simulations are presented to support the analytical results. The convergence and consistency of the proposed method are also discussed. The proposed method converges unconditionally while the many classical methods in the literature do not possess this property. In this regard, our proposed method can be considered as a reliable tool for studying the dynamics of HFMD.

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