Shumaila Azam¹, Nauman Ahmed^1,6, Ali Raza², Muhammad Sajid Iqbal¹, Muhammad Rafiq³, Ilyas Khan^4,*, Kottakkaran Sooppy Nisar⁵, Muhammad Ozair Ahmad¹, Zafar Iqbal^1,6

CMC-Computers, Materials & Continua, Vol.67, No.3, pp. 2933-2953, 2021, DOI:10.32604/cmc.2021.012396

Abstract Recently, the world is facing the terror of the novel corona-virus, termed as COVID-19. Various health institutes and researchers are continuously striving to control this pandemic. In this article, the SEIAR (susceptible, exposed, infected, symptomatically infected, asymptomatically infected and recovered) infection model of COVID-19 with a constant rate of advection is studied for the disease propagation. A simple model of the disease is extended to an advection model by accommodating the advection process and some appropriate parameters in the system. The continuous model is transposed into a discrete numerical model by discretizing the domains, finitely. To analyze the disease dynamics,… More >

Muhammad Saqib¹, Muhammad Shoaib Arif^2,*, Shahid Hasnain³, Daoud S. Mashat⁴

CMC-Computers, Materials & Continua, Vol.67, No.2, pp. 2161-2183, 2021, DOI:10.32604/cmc.2021.014507

Abstract The efficiency of solving computationally partial differential equations can be profoundly highlighted by the creation of precise, higher-order compact numerical scheme that results in truly outstanding accuracy at a given cost. The objective of this article is to develop a highly accurate novel algorithm for two dimensional non-linear Burgers Huxley (BH) equations. The proposed compact numerical scheme is found to be free of superiors approximate oscillations across discontinuities, and in a smooth flow region, it efficiently obtained a high-order accuracy. In particular, two classes of higher-order compact finite difference schemes are taken into account and compared based on their computational… More >

Zejian Zhang¹, Dawei Wang^2,*, Xiao-Zhi Gao³

Intelligent Automation & Soft Computing, Vol.27, No.1, pp. 173-189, 2021, DOI:10.32604/iasc.2021.012805

Abstract The interval type-2 fuzzy sets can describe nonlinear plants with uncertain parameters. It exists in nonlinearity. The parameter uncertainties extensively exist in the nonlinear practical Networked Control Systems (NCSs), and it is paramount to investigate the stabilization of the NCSs on account of the section type-2 fuzzy systems. Notice that most of the existing research work is only on account of the convention Parallel Distribution Compensation (PDC). For overcoming the weak point of the PDC and acquire certain guard stability conditions, the state tickling regulator under imperfect premise matching can be constructed to steady the NCSs using the section type-2… More >

Isa Abdullahi Baba^1,*, Bashir Ahmad Nasidi¹, Dumitru Baleanu^2,3,4

CMC-Computers, Materials & Continua, Vol.66, No.3, pp. 3089-3106, 2021, DOI:10.32604/cmc.2021.012301

Abstract As the corona virus (COVID-19) pandemic ravages socio-economic activities in addition to devastating infectious and fatal consequences, optimal control strategy is an effective measure that neutralizes the scourge to its lowest ebb. In this paper, we present a mathematical model for the dynamics of COVID-19, and then we added an optimal control function to the model in order to effectively control the outbreak. We incorporate three main control efforts (isolation, quarantine and hospitalization) into the model aimed at controlling the spread of the pandemic. These efforts are further subdivided into five functions; u₁(t) (isolation of the susceptible communities), u₂(t) (contact… More >

Olumuyiwa J. Peter¹, Amjad S. Shaikh^2,*, Mohammed O. Ibrahim¹, Kottakkaran Sooppy Nisar³, Dumitru Baleanu^4,5,6, Ilyas Khan⁷, Adesoye I. Abioye¹

CMC-Computers, Materials & Continua, Vol.66, No.2, pp. 1823-1848, 2021, DOI:10.32604/cmc.2020.012314

Abstract We propose a mathematical model of the coronavirus disease 2019 (COVID-19) to investigate the transmission and control mechanism of the disease in the community of Nigeria. Using stability theory of differential equations, the qualitative behavior of model is studied. The pandemic indicator represented by basic reproductive number R₀ is obtained from the largest eigenvalue of the next-generation matrix. Local as well as global asymptotic stability conditions for the disease-free and pandemic equilibrium are obtained which determines the conditions to stabilize the exponential spread of the disease. Further, we examined this model by using Atangana–Baleanu fractional derivative operator and existence criteria… More >

Liaquat Ali Lund^1,2, Zurni Omar¹, Sumera Dero^1,3, Yuming Chu^4,5, Ilyas Khan^6,*, Kottakkaran Sooppy Nisar⁷

CMC-Computers, Materials & Continua, Vol.66, No.2, pp. 1963-1975, 2021, DOI:10.32604/cmc.2020.011976

Abstract The unsteady magnetohydrodynamic (MHD) flow on a horizontal preamble surface with hybrid nanoparticles in the presence of the first order velocity and thermal slip conditions are investigated. Alumina (Al₂O₃) and copper (Cu) are considered as hybrid nanoparticles that have been dispersed in water in order to make hybrid nanofluid (Cu − Al₂O₃/water). The system of similarity equations is derived from the system of partial differential equations (PDEs) by using variables of similarity, and their solutions are gotten with shooting method in the Maple software. In certain ranges of unsteadiness and magnetic parameters, the presence of dual solutions can be found.… More >

Berat Karaagac^{1, 2}, Kolade Matthew Owolabi^{1, 3, *}, Kottakkaran Sooppy Nisar⁴

CMC-Computers, Materials & Continua, Vol.65, No.3, pp. 1905-1924, 2020, DOI:10.32604/cmc.2020.011623

Abstract Illicit drug use is a significant problem that causes great material and moral losses and threatens the future of the society. For this reason, illicit drug use and related crimes are the most significant criminal cases examined by scientists. This paper aims at modeling the illegal drug use using the Atangana-Baleanu fractional derivative with Mittag-Leffler kernel. Also, in this work, the existence and uniqueness of solutions of the fractional-order Illicit drug use model are discussed via Picard-Lindelöf theorem which provides successive approximations using a convergent sequence. Then the stability analysis for both disease-free and endemic equilibrium states is conducted. A… More >

Muhammad Naveed^{1, *}, Dumitru Baleanu^{2, 3, 4}, Muhammad Rafiq⁵, Ali Raza⁶, Atif Hassan Soori¹, Nauman Ahmed⁷

CMC-Computers, Materials & Continua, Vol.65, No.1, pp. 225-241, 2020, DOI:10.32604/cmc.2020.011534

Abstract Mathematical delay modelling has a significant role in the different disciplines such as behavioural, social, physical, biological engineering, and bio-mathematical sciences. The present work describes mathematical formulation for the transmission mechanism of a novel coronavirus (COVID-19). Due to the unavailability of vaccines for the coronavirus worldwide, delay factors such as social distance, quarantine, travel restrictions, extended holidays, hospitalization, and isolation have contributed to controlling the coronavirus epidemic. We have analysed the reproduction number and its sensitivity to parameters. If, More >

Muhammad Naveed¹, Muhammad Rafiq², Ali Raza³, Nauman Ahmed⁴, Ilyas Khan^{5, *}, Kottakkaran Sooppy Nisar⁶, Atif Hassan Soori¹

CMC-Computers, Materials & Continua, Vol.64, No.3, pp. 1401-1414, 2020, DOI:10.32604/cmc.2020.011314

Abstract In this manuscript, the mathematical analysis of corona virus model with time delay effect is studied. Mathematical modelling of infectious diseases has substantial role in the different disciplines such as biological, engineering, physical, social, behavioural problems and many more. Most of infectious diseases are dreadful such as HIV/AIDS, Hepatitis and 2019-nCov. Unfortunately, due to the non-availability of vaccine for 2019- nCov around the world, the delay factors like, social distancing, quarantine, travel restrictions, holidays extension, hospitalization and isolation are used as key tools to control the pandemic of 2019-nCov. We have analysed the reproduction number R_nCov of delayed model. Two… More >

Lennon Ó Náraigh^{1, *}, Daniel R. Jansen van Vuuren²

FDMP-Fluid Dynamics & Materials Processing, Vol.16, No.2, pp. 383-410, 2020, DOI:10.32604/fdmp.2020.09265

Abstract In this article we use analytical and numerical modeling to describe parallel viscous two-phase flows in microchannels. The focus is on idealized two-dimensional geometries, with a view to validating the various methodologies for future work in three dimensions. In the first instance, we use analytical Orr-Sommerfeld theory to describe the linear instability which governs the formation of small-amplitude waves in such systems. We then compare the results of this analysis with an in-house Computational Fluid Dynamics (CFD) solver called TPLS. Excellent agreement between the theoretical analysis and TPLS is obtained in the regime of small-amplitude waves. We continue the numerical… More >