Matematik Bölümü Yayın Koleksiyonu

Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/413

Browse

Filters

2022 - 20232

Settings

Author: search.filters.author.Ahmad, Muhammad OzairSubject: search.filters.subject.Convergence

Search Results

Now showing 1 - 2 of 2
  • Article
    Citation - WoS: 15
    Design and Numerical Analysis of Fuzzy Nonstandard Computational Methods for the Solution of Rumor Based Fuzzy Epidemic Model
    (Elsevier, 2022) Rafiq, Muhammad; Ahmed, Nauman; Baleanu, Dumitru; Raza, Ali; Ahmad, Muhammad Ozair; Iqbal, Muhammad; Dayan, Fazal
    This model extends the classical epidemic model for cyber consumerism by introducing fuzziness to the model. Fuzziness arises due to insufficient knowledge, experimental errors, operating conditions and parameters that provide inaccurate information. The concepts of confused, escapers and recovered consumers are uncertain due to the different degrees of confusion, escaping and recovery among the individuals of the cyber consumers. The differences can arise, when the cyber consumers under the consideration having distinct habits, customs and different age groups have different degrees of resistance, etc. The chance of transmission of rumors and recovery rates are considered as fuzzy numbers. A rumor-free and two rumor existing-endemic equilibrium points have been derived for the studied model. The model is then solved numerically with fuzzy forward Euler and fuzzy nonstandard finite difference (FNSFD) methods respectively. The numerical and simulation results show that the proposed FNSFD technique is an efficient and reliable tool to deal with such type of dynamical system. (c) 2022 Elsevier B.V. All rights reserved.
  • Article
    Citation - WoS: 2
    Citation - Scopus: 2
    Computational Investigation of Hand Foot Mouth Disease Dynamics With Fuzziness
    (Tech Science Press, 2023) Dayan, Fazal; Ahmed, Nauman; Rafiq, Muhammad; Raza, Ali; Ahmad, Muhammad Ozair; Baleanu, Dumitru
    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.