Muhammad Shoaib Arif^1,2,*, Kamaleldin Abodayeh¹, Yasir Nawaz²

CMES-Computer Modeling in Engineering & Sciences, Vol.139, No.3, pp. 3417-3434, 2024, DOI:10.32604/cmes.2024.046944 - 11 March 2024

Abstract This study focuses on the urgent requirement for improved accuracy in disease modeling by introducing a new computational framework called the Hybrid SIR-Fuzzy Model. By integrating the traditional Susceptible-Infectious-Recovered (SIR) model with fuzzy logic, our method effectively addresses the complex nature of epidemic dynamics by accurately accounting for uncertainties and imprecisions in both data and model parameters. The main aim of this research is to provide a model for disease transmission using fuzzy theory, which can successfully address uncertainty in mathematical modeling. Our main emphasis is on the imprecise transmission rate parameter, utilizing a three-part… More >

Muhammad Shoaib Arif^1,2,*, Kamaleldin Abodayeh¹, Yasir Nawaz²

CMES-Computer Modeling in Engineering & Sciences, Vol.138, No.2, pp. 1405-1425, 2024, DOI:10.32604/cmes.2023.028946 - 17 November 2023

Abstract This work aimed to construct an epidemic model with fuzzy parameters. Since the classical epidemic model does not elaborate on the successful interaction of susceptible and infective people, the constructed fuzzy epidemic model discusses the more detailed versions of the interactions between infective and susceptible people. The next-generation matrix approach is employed to find the reproduction number of a deterministic model. The sensitivity analysis and local stability analysis of the system are also provided. For solving the fuzzy epidemic model, a numerical scheme is constructed which consists of three time levels. The numerical scheme has More >

Fei Li¹, Haci Mehmet Baskonus^2,*, S. Kumbinarasaiah³, G. Manohara³, Wei Gao⁴, Esin Ilhan⁵

CMES-Computer Modeling in Engineering & Sciences, Vol.137, No.3, pp. 2381-2408, 2023, DOI:10.32604/cmes.2023.028069 - 03 August 2023

Abstract This article considers three types of biological systems: the dengue fever disease model, the COVID-19 virus model, and the transmission of Tuberculosis model. The new technique of creating the integration matrix for the Bernoulli wavelets is applied. Also, the novel method proposed in this paper is called the Bernoulli wavelet collocation scheme (BWCM). All three models are in the form system of coupled ordinary differential equations without an exact solution. These systems are converted into a system of algebraic equations using the Bernoulli wavelet collocation scheme. The numerical wave distributions of these governing models are More >

Yu-Ming Chu¹, Sobia Sultana², Saima Rashid^3,*, Mohammed Shaaf Alharthi⁴

CMES-Computer Modeling in Engineering & Sciences, Vol.137, No.3, pp. 2427-2464, 2023, DOI:10.32604/cmes.2023.028771 - 03 August 2023

Abstract Various data sets showing the prevalence of numerous viral diseases have demonstrated that the transmission is not truly homogeneous. Two examples are the spread of Spanish flu and COVID-19. The aim of this research is to develop a comprehensive nonlinear stochastic model having six cohorts relying on ordinary differential equations via piecewise fractional differential operators. Firstly, the strength number of the deterministic case is carried out. Then, for the stochastic model, we show that there is a critical number that can predict virus persistence and infection eradication. Because of the peculiarity of More >

Mudassir Shams¹, Nasreen Kausar^2,*, Shams Forruque Ahmed³, Irfan Anjum Badruddin⁴, Syed Javed⁴

CMC-Computers, Materials & Continua, Vol.74, No.3, pp. 5331-5347, 2023, DOI:10.32604/cmc.2023.033528 - 28 December 2022

Abstract A fifth-order family of an iterative method for solving systems of nonlinear equations and highly nonlinear boundary value problems has been developed in this paper. Convergence analysis demonstrates that the local order of convergence of the numerical method is five. The computer algebra system CAS-Maple, Mathematica, or MATLAB was the primary tool for dealing with difficult problems since it allows for the handling and manipulation of complex mathematical equations and other mathematical objects. Several numerical examples are provided to demonstrate the properties of the proposed rapidly convergent algorithms. A dynamic evaluation of the presented methods More >

Idrees Khan^1,2, Tiri Chinyoka^1,2,*, Andrew Gill³

FDMP-Fluid Dynamics & Materials Processing, Vol.19, No.3, pp. 767-781, 2023, DOI:10.32604/fdmp.2022.021921 - 29 September 2022

Abstract The paper explores the gravity-driven flow of the thin film of a viscoelastic-fluid-based nanofluids (VFBN) along an inclined plane under non-isothermal conditions and subjected to convective cooling at the free-surface. The Newton’s law of cooling is used to model the convective heat-exchange with the ambient at the free-surface. The Giesekus viscoelastic constitutive model, with appropriate modifications to account for non-isothermal effects, is employed to describe the polymeric effects. The unsteady and coupled non-linear partial differential equations (PDEs) describing the model problem are obtained and solved via efficient semi-implicit numerical schemes based on finite difference methods More >

Asad Ejaz¹, Yasir Nawaz¹, Muhammad Shoaib Arif^1,3,*, Daoud S. Mashat², Kamaleldin Abodayeh³

CMES-Computer Modeling in Engineering & Sciences, Vol.132, No.2, pp. 489-506, 2022, DOI:10.32604/cmes.2022.019440 - 15 June 2022

Abstract The present study is concerned with formulating a predator-prey eco-epidemiological mathematical model assuming that an infection exists in the predator species. The two classes of predator species (susceptible and infected) compete for the same sources available in the environment with the predation option. It is assumed that the disease does not spread vertically. The proposed model is analyzed for the stability of the coexistence of the predators and prey. The fixed points are carried out, and the coexisting fixed point is studied in detail by constructing the Lyapunov function. The movement of species in search… More >

Rohul Amin¹, Şuayip Yüzbası^2,*, Shah Nazir³

CMES-Computer Modeling in Engineering & Sciences, Vol.131, No.2, pp. 639-653, 2022, DOI:10.32604/cmes.2022.019154 - 14 March 2022

Abstract In this paper, Haar collocation algorithm is developed for the solution of first-order of HIV infection CD4⁺ T-Cells model. In this technique, the derivative in the nonlinear model is approximated by utilizing Haar functions. The value of the unknown function is obtained by the process of integration. Error estimation is also discussed, which aims to reduce the error of numerical solutions. The numerical results show that the method is simply applicable. The results are compared with Runge-Kutta technique, Bessel collocation technique, LADM-Pade and Galerkin technique available in the literature. The results show that the Haar technique More >

Mudassir Shams¹, Naila Rafiq², Nasreen Kausar³, Nazir Ahmad Mir², Ahmad Alalyani^4,*

Computer Systems Science and Engineering, Vol.42, No.2, pp. 689-701, 2022, DOI:10.32604/csse.2022.022269 - 04 January 2022

Abstract In this study, we construct a family of single root finding method of optimal order four and then generalize this family for estimating of all roots of non-linear equation simultaneously. Convergence analysis proves that the local order of convergence is four in case of single root finding iterative method and six for simultaneous determination of all roots of non-linear equation. Some non-linear equations are taken from physics, chemistry and engineering to present the performance and efficiency of the newly constructed method. Some real world applications are taken from fluid mechanics, i.e., fluid permeability in biogels More >

Mudassir Shams^1,*, Naila Rafiq², Nazir Ahmad Mir^1,2, Babar Ahmad³, Saqib Abbasi¹, Mutee-Ur-Rehman Kayani¹

Computer Systems Science and Engineering, Vol.36, No.3, pp. 493-507, 2021, DOI:10.32604/csse.2021.014476 - 18 January 2021

Abstract In this research article, we interrogate two new modifications in inverse Weierstrass iterative method for estimating all roots of non-linear equation simultaneously. These modifications enables us to accelerate the convergence order of inverse Weierstrass method from 2 to 3. Convergence analysis proves that the orders of convergence of the two newly constructed inverse methods are 3. Using computer algebra system Mathematica, we find the lower bound of the convergence order and verify it theoretically. Dynamical planes of the inverse simultaneous methods and classical iterative methods are generated using MATLAB (R2011b), to present the global convergence More >